Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups
We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T>0 by taking into account the orbit of the initial value under the semigroup for t in [0,T], measured in a suitable norm. We state a s...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kruse, Karsten - 1984- [verfasserIn] Seifert, Christian - 1985- [verfasserIn] |
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| Körperschaften: |
| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Rechteinformationen: |
Open Access Namensnennung 4.0 International ; CC BY 4.0 |
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| Schlagwörter: |
Final state observability estimate |
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| Anmerkung: |
Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik |
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| Übergeordnetes Werk: |
Enthalten in: Semigroup forum - New York, NY : Springer, 1970, 00(2023), 00, Seite 00 |
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| Übergeordnetes Werk: |
volume:00 ; year:2023 ; number:00 ; pages:00 |
| Links: |
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| DOI / URN: |
urn:nbn:de:gbv:830-882.0215289 10.15480/882.5032 10.1007/s00233-023-10346-1 |
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| Katalog-ID: |
1842496832 |
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| 264 | 1 | |c 2023 | |
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| 520 | |a We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T>0 by taking into account the orbit of the initial value under the semigroup for t in [0,T], measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauß–Weierstraß semigroup and the Ornstein-Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the case of Banach spaces. | ||
| 540 | |q DE-830 |a Namensnennung 4.0 International |f CC BY 4.0 |2 cc |u https://creativecommons.org/licenses/by/4.0/ | ||
| 650 | 7 | |a Final state observability estimate |2 DSpace | |
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urn:nbn:de:gbv:830-882.0215289 urn 10.15480/882.5032 doi 10.1007/s00233-023-10346-1 doi 11420/15090 hdl (DE-627)1842496832 (DE-599)KXP1842496832 DE-627 ger DE-627 rda eng 510: Mathematik Kruse, Karsten 1984- verfasserin (DE-588)1055972765 (DE-627)79299843X (DE-576)411984411 aut Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups Karsten Kruse, Christian Seifert 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T>0 by taking into account the orbit of the initial value under the semigroup for t in [0,T], measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauß–Weierstraß semigroup and the Ornstein-Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the case of Banach spaces. DE-830 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Final state observability estimate DSpace Bi-continuous semigroups DSpace Cost-uniform approximate null-controllability DSpace Saks space DSpace Mixed topology DSpace Seifert, Christian 1985- verfasserin (DE-588)1030178798 (DE-627)734893256 (DE-576)377989959 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Semigroup forum New York, NY : Springer, 1970 00(2023), 00, Seite 00 Online-Ressource (DE-627)300187009 (DE-600)1481770-6 (DE-576)094950245 1432-2137 nnns volume:00 year:2023 number:00 pages:00 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0215289 Resolving-System kostenfrei https://doi.org/10.15480/882.5032 Resolving-System kostenfrei http://hdl.handle.net/11420/15090 Resolving-System kostenfrei https://doi.org/10.1007/s00233-023-10346-1 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 DSpace AR 00 2023 00 00 045F 510: Mathematik 23 01 0830 4308427258 tuhh Elektronischer Volltext f z 13-04-23 23 01 0830 https://doi.org/10.15480/882.5032 LF 23 01 0830 tuhh 23 01 0830 tubdok |
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urn:nbn:de:gbv:830-882.0215289 urn 10.15480/882.5032 doi 10.1007/s00233-023-10346-1 doi 11420/15090 hdl (DE-627)1842496832 (DE-599)KXP1842496832 DE-627 ger DE-627 rda eng 510: Mathematik Kruse, Karsten 1984- verfasserin (DE-588)1055972765 (DE-627)79299843X (DE-576)411984411 aut Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups Karsten Kruse, Christian Seifert 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T>0 by taking into account the orbit of the initial value under the semigroup for t in [0,T], measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauß–Weierstraß semigroup and the Ornstein-Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the case of Banach spaces. DE-830 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Final state observability estimate DSpace Bi-continuous semigroups DSpace Cost-uniform approximate null-controllability DSpace Saks space DSpace Mixed topology DSpace Seifert, Christian 1985- verfasserin (DE-588)1030178798 (DE-627)734893256 (DE-576)377989959 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Semigroup forum New York, NY : Springer, 1970 00(2023), 00, Seite 00 Online-Ressource (DE-627)300187009 (DE-600)1481770-6 (DE-576)094950245 1432-2137 nnns volume:00 year:2023 number:00 pages:00 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0215289 Resolving-System kostenfrei https://doi.org/10.15480/882.5032 Resolving-System kostenfrei http://hdl.handle.net/11420/15090 Resolving-System kostenfrei https://doi.org/10.1007/s00233-023-10346-1 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 DSpace AR 00 2023 00 00 045F 510: Mathematik 23 01 0830 4308427258 tuhh Elektronischer Volltext f z 13-04-23 23 01 0830 https://doi.org/10.15480/882.5032 LF 23 01 0830 tuhh 23 01 0830 tubdok |
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urn:nbn:de:gbv:830-882.0215289 urn 10.15480/882.5032 doi 10.1007/s00233-023-10346-1 doi 11420/15090 hdl (DE-627)1842496832 (DE-599)KXP1842496832 DE-627 ger DE-627 rda eng 510: Mathematik Kruse, Karsten 1984- verfasserin (DE-588)1055972765 (DE-627)79299843X (DE-576)411984411 aut Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups Karsten Kruse, Christian Seifert 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T>0 by taking into account the orbit of the initial value under the semigroup for t in [0,T], measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauß–Weierstraß semigroup and the Ornstein-Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the case of Banach spaces. DE-830 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Final state observability estimate DSpace Bi-continuous semigroups DSpace Cost-uniform approximate null-controllability DSpace Saks space DSpace Mixed topology DSpace Seifert, Christian 1985- verfasserin (DE-588)1030178798 (DE-627)734893256 (DE-576)377989959 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Semigroup forum New York, NY : Springer, 1970 00(2023), 00, Seite 00 Online-Ressource (DE-627)300187009 (DE-600)1481770-6 (DE-576)094950245 1432-2137 nnns volume:00 year:2023 number:00 pages:00 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0215289 Resolving-System kostenfrei https://doi.org/10.15480/882.5032 Resolving-System kostenfrei http://hdl.handle.net/11420/15090 Resolving-System kostenfrei https://doi.org/10.1007/s00233-023-10346-1 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 DSpace AR 00 2023 00 00 045F 510: Mathematik 23 01 0830 4308427258 tuhh Elektronischer Volltext f z 13-04-23 23 01 0830 https://doi.org/10.15480/882.5032 LF 23 01 0830 tuhh 23 01 0830 tubdok |
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urn:nbn:de:gbv:830-882.0215289 urn 10.15480/882.5032 doi 10.1007/s00233-023-10346-1 doi 11420/15090 hdl (DE-627)1842496832 (DE-599)KXP1842496832 DE-627 ger DE-627 rda eng 510: Mathematik Kruse, Karsten 1984- verfasserin (DE-588)1055972765 (DE-627)79299843X (DE-576)411984411 aut Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups Karsten Kruse, Christian Seifert 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T>0 by taking into account the orbit of the initial value under the semigroup for t in [0,T], measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauß–Weierstraß semigroup and the Ornstein-Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the case of Banach spaces. DE-830 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Final state observability estimate DSpace Bi-continuous semigroups DSpace Cost-uniform approximate null-controllability DSpace Saks space DSpace Mixed topology DSpace Seifert, Christian 1985- verfasserin (DE-588)1030178798 (DE-627)734893256 (DE-576)377989959 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Semigroup forum New York, NY : Springer, 1970 00(2023), 00, Seite 00 Online-Ressource (DE-627)300187009 (DE-600)1481770-6 (DE-576)094950245 1432-2137 nnns volume:00 year:2023 number:00 pages:00 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0215289 Resolving-System kostenfrei https://doi.org/10.15480/882.5032 Resolving-System kostenfrei http://hdl.handle.net/11420/15090 Resolving-System kostenfrei https://doi.org/10.1007/s00233-023-10346-1 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 DSpace AR 00 2023 00 00 045F 510: Mathematik 23 01 0830 4308427258 tuhh Elektronischer Volltext f z 13-04-23 23 01 0830 https://doi.org/10.15480/882.5032 LF 23 01 0830 tuhh 23 01 0830 tubdok |
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urn:nbn:de:gbv:830-882.0215289 urn 10.15480/882.5032 doi 10.1007/s00233-023-10346-1 doi 11420/15090 hdl (DE-627)1842496832 (DE-599)KXP1842496832 DE-627 ger DE-627 rda eng 510: Mathematik Kruse, Karsten 1984- verfasserin (DE-588)1055972765 (DE-627)79299843X (DE-576)411984411 aut Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups Karsten Kruse, Christian Seifert 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik DE-830 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T>0 by taking into account the orbit of the initial value under the semigroup for t in [0,T], measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauß–Weierstraß semigroup and the Ornstein-Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the case of Banach spaces. DE-830 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Final state observability estimate DSpace Bi-continuous semigroups DSpace Cost-uniform approximate null-controllability DSpace Saks space DSpace Mixed topology DSpace Seifert, Christian 1985- verfasserin (DE-588)1030178798 (DE-627)734893256 (DE-576)377989959 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg Institut für Mathematik (DE-588)1170812678 (DE-627)1040092225 (DE-576)512657130 oth Enthalten in Semigroup forum New York, NY : Springer, 1970 00(2023), 00, Seite 00 Online-Ressource (DE-627)300187009 (DE-600)1481770-6 (DE-576)094950245 1432-2137 nnns volume:00 year:2023 number:00 pages:00 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0215289 Resolving-System kostenfrei https://doi.org/10.15480/882.5032 Resolving-System kostenfrei http://hdl.handle.net/11420/15090 Resolving-System kostenfrei https://doi.org/10.1007/s00233-023-10346-1 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 DSpace AR 00 2023 00 00 045F 510: Mathematik 23 01 0830 4308427258 tuhh Elektronischer Volltext f z 13-04-23 23 01 0830 https://doi.org/10.15480/882.5032 LF 23 01 0830 tuhh 23 01 0830 tubdok |
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final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups |
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Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups |
| abstract |
We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T>0 by taking into account the orbit of the initial value under the semigroup for t in [0,T], measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauß–Weierstraß semigroup and the Ornstein-Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the case of Banach spaces. Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik |
| abstractGer |
We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T>0 by taking into account the orbit of the initial value under the semigroup for t in [0,T], measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauß–Weierstraß semigroup and the Ornstein-Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the case of Banach spaces. Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik |
| abstract_unstemmed |
We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T>0 by taking into account the orbit of the initial value under the semigroup for t in [0,T], measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauß–Weierstraß semigroup and the Ornstein-Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the case of Banach spaces. Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik |
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Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups |
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http://nbn-resolving.de/urn:nbn:de:gbv:830-882.0215289 https://doi.org/10.15480/882.5032 http://hdl.handle.net/11420/15090 https://doi.org/10.1007/s00233-023-10346-1 |
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Seifert, Christian 1985- Technische Universität Hamburg Technische Universität Hamburg Institut für Mathematik |
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Kruse, Karsten Seifert, Christian University of Technology (Hamburg) TU Hamburg Technical University (Hamburg) Université de Technologie de Hambourg Hamburg University of Technology Technische Universität Hamburg Institute of Mathematics (Hamburg) Institut E-10 Technische Universität Hamburg. Studiendekanat Elektrotechnik, Informatik und Mathematik. Institut für Mathematik Institut für Mathematik (Hamburg) Technische Universität Hamburg. Institut E-10 Technische Universität Hamburg. Institute of Mathematics Technische Universität Hamburg. Institut für Mathematik |
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Kruse, Karsten Seifert, Christian University of Technology (Hamburg) TU Hamburg Technical University (Hamburg) Université de Technologie de Hambourg Hamburg University of Technology Technische Universität Hamburg Institute of Mathematics (Hamburg) Institut E-10 Technische Universität Hamburg. Studiendekanat Elektrotechnik, Informatik und Mathematik. Institut für Mathematik Institut für Mathematik (Hamburg) Technische Universität Hamburg. Institut E-10 Technische Universität Hamburg. Institute of Mathematics Technische Universität Hamburg. Institut für Mathematik |
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Kruse, Karsten Seifert, Christian University of Technology (Hamburg) TU Hamburg Technical University (Hamburg) Université de Technologie de Hambourg Hamburg University of Technology Technische Universität Hamburg Institute of Mathematics (Hamburg) Institut E-10 Technische Universität Hamburg. Studiendekanat Elektrotechnik, Informatik und Mathematik. Institut für Mathematik Institut für Mathematik (Hamburg) Technische Universität Hamburg. Institut E-10 Technische Universität Hamburg. Institute of Mathematics Technische Universität Hamburg. Institut für Mathematik |
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| score |
7.3991747 |