On the convergence of regular families of cardinal interpolators
Abstract In this article, we develop a one parameter family of cardinal interpolants associated to a function ϕ. The main theorem gives conditions on ϕ and the parameter that allow Paley-Wiener functions to be recovered from their samples on the integer lattice $\mathbb {Z}^{n}$. Our methods unify p...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ledford, Jeff [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Advances in computational mathematics - Bussum : Baltzer Science Publ., 1993, 41(2014), 2 vom: 29. Mai, Seite 357-371 |
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| Übergeordnetes Werk: |
volume:41 ; year:2014 ; number:2 ; day:29 ; month:05 ; pages:357-371 |
| Links: |
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| DOI / URN: |
10.1007/s10444-014-9361-4 |
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| Katalog-ID: |
SPR01010898X |
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| 245 | 1 | 0 | |a On the convergence of regular families of cardinal interpolators |
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| 520 | |a Abstract In this article, we develop a one parameter family of cardinal interpolants associated to a function ϕ. The main theorem gives conditions on ϕ and the parameter that allow Paley-Wiener functions to be recovered from their samples on the integer lattice $\mathbb {Z}^{n}$. Our methods unify previous work done on splines and the Gaussian and provide new examples of this phenomenon, including two families of multiquadrics. | ||
| 650 | 4 | |a Cardinal interpolation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Multiquadric interpolation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Multivariate interpolation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Paley-Wiener functions |7 (dpeaa)DE-He213 | |
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10.1007/s10444-014-9361-4 doi (DE-627)SPR01010898X (SPR)s10444-014-9361-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Ledford, Jeff verfasserin aut On the convergence of regular families of cardinal interpolators 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this article, we develop a one parameter family of cardinal interpolants associated to a function ϕ. The main theorem gives conditions on ϕ and the parameter that allow Paley-Wiener functions to be recovered from their samples on the integer lattice $\mathbb {Z}^{n}$. Our methods unify previous work done on splines and the Gaussian and provide new examples of this phenomenon, including two families of multiquadrics. Cardinal interpolation (dpeaa)DE-He213 Multiquadric interpolation (dpeaa)DE-He213 Multivariate interpolation (dpeaa)DE-He213 Paley-Wiener functions (dpeaa)DE-He213 Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 41(2014), 2 vom: 29. Mai, Seite 357-371 (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:41 year:2014 number:2 day:29 month:05 pages:357-371 https://dx.doi.org/10.1007/s10444-014-9361-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 31.76 ASE AR 41 2014 2 29 05 357-371 |
| spelling |
10.1007/s10444-014-9361-4 doi (DE-627)SPR01010898X (SPR)s10444-014-9361-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Ledford, Jeff verfasserin aut On the convergence of regular families of cardinal interpolators 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this article, we develop a one parameter family of cardinal interpolants associated to a function ϕ. The main theorem gives conditions on ϕ and the parameter that allow Paley-Wiener functions to be recovered from their samples on the integer lattice $\mathbb {Z}^{n}$. Our methods unify previous work done on splines and the Gaussian and provide new examples of this phenomenon, including two families of multiquadrics. Cardinal interpolation (dpeaa)DE-He213 Multiquadric interpolation (dpeaa)DE-He213 Multivariate interpolation (dpeaa)DE-He213 Paley-Wiener functions (dpeaa)DE-He213 Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 41(2014), 2 vom: 29. Mai, Seite 357-371 (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:41 year:2014 number:2 day:29 month:05 pages:357-371 https://dx.doi.org/10.1007/s10444-014-9361-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 31.76 ASE AR 41 2014 2 29 05 357-371 |
| allfields_unstemmed |
10.1007/s10444-014-9361-4 doi (DE-627)SPR01010898X (SPR)s10444-014-9361-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Ledford, Jeff verfasserin aut On the convergence of regular families of cardinal interpolators 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this article, we develop a one parameter family of cardinal interpolants associated to a function ϕ. The main theorem gives conditions on ϕ and the parameter that allow Paley-Wiener functions to be recovered from their samples on the integer lattice $\mathbb {Z}^{n}$. Our methods unify previous work done on splines and the Gaussian and provide new examples of this phenomenon, including two families of multiquadrics. Cardinal interpolation (dpeaa)DE-He213 Multiquadric interpolation (dpeaa)DE-He213 Multivariate interpolation (dpeaa)DE-He213 Paley-Wiener functions (dpeaa)DE-He213 Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 41(2014), 2 vom: 29. Mai, Seite 357-371 (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:41 year:2014 number:2 day:29 month:05 pages:357-371 https://dx.doi.org/10.1007/s10444-014-9361-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 31.76 ASE AR 41 2014 2 29 05 357-371 |
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10.1007/s10444-014-9361-4 doi (DE-627)SPR01010898X (SPR)s10444-014-9361-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Ledford, Jeff verfasserin aut On the convergence of regular families of cardinal interpolators 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this article, we develop a one parameter family of cardinal interpolants associated to a function ϕ. The main theorem gives conditions on ϕ and the parameter that allow Paley-Wiener functions to be recovered from their samples on the integer lattice $\mathbb {Z}^{n}$. Our methods unify previous work done on splines and the Gaussian and provide new examples of this phenomenon, including two families of multiquadrics. Cardinal interpolation (dpeaa)DE-He213 Multiquadric interpolation (dpeaa)DE-He213 Multivariate interpolation (dpeaa)DE-He213 Paley-Wiener functions (dpeaa)DE-He213 Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 41(2014), 2 vom: 29. Mai, Seite 357-371 (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:41 year:2014 number:2 day:29 month:05 pages:357-371 https://dx.doi.org/10.1007/s10444-014-9361-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 31.76 ASE AR 41 2014 2 29 05 357-371 |
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Enthalten in Advances in computational mathematics 41(2014), 2 vom: 29. Mai, Seite 357-371 volume:41 year:2014 number:2 day:29 month:05 pages:357-371 |
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Cardinal interpolation Multiquadric interpolation Multivariate interpolation Paley-Wiener functions |
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Advances in computational mathematics |
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Ledford, Jeff @@aut@@ |
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Ledford, Jeff |
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Ledford, Jeff ddc 510 bkl 31.76 misc Cardinal interpolation misc Multiquadric interpolation misc Multivariate interpolation misc Paley-Wiener functions On the convergence of regular families of cardinal interpolators |
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510 ASE 31.76 bkl On the convergence of regular families of cardinal interpolators Cardinal interpolation (dpeaa)DE-He213 Multiquadric interpolation (dpeaa)DE-He213 Multivariate interpolation (dpeaa)DE-He213 Paley-Wiener functions (dpeaa)DE-He213 |
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on the convergence of regular families of cardinal interpolators |
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On the convergence of regular families of cardinal interpolators |
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Abstract In this article, we develop a one parameter family of cardinal interpolants associated to a function ϕ. The main theorem gives conditions on ϕ and the parameter that allow Paley-Wiener functions to be recovered from their samples on the integer lattice $\mathbb {Z}^{n}$. Our methods unify previous work done on splines and the Gaussian and provide new examples of this phenomenon, including two families of multiquadrics. |
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Abstract In this article, we develop a one parameter family of cardinal interpolants associated to a function ϕ. The main theorem gives conditions on ϕ and the parameter that allow Paley-Wiener functions to be recovered from their samples on the integer lattice $\mathbb {Z}^{n}$. Our methods unify previous work done on splines and the Gaussian and provide new examples of this phenomenon, including two families of multiquadrics. |
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Abstract In this article, we develop a one parameter family of cardinal interpolants associated to a function ϕ. The main theorem gives conditions on ϕ and the parameter that allow Paley-Wiener functions to be recovered from their samples on the integer lattice $\mathbb {Z}^{n}$. Our methods unify previous work done on splines and the Gaussian and provide new examples of this phenomenon, including two families of multiquadrics. |
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