Duals of Frame Sequences
Abstract Frames provide unconditional basis-like, but generally nonunique, representations of vectors in a Hilbert space H. The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, a...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Heil, Christopher [verfasserIn] Koo, Yoo Young [verfasserIn] Lim, Jae Kun [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2008 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Acta applicandae mathematicae - [S.l.] : Proquest, 1983, 107(2008), 1-3 vom: 16. Dez., Seite 75-90 |
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| Übergeordnetes Werk: |
volume:107 ; year:2008 ; number:1-3 ; day:16 ; month:12 ; pages:75-90 |
| Links: |
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| DOI / URN: |
10.1007/s10440-008-9410-4 |
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| Katalog-ID: |
SPR010079173 |
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| 520 | |a Abstract Frames provide unconditional basis-like, but generally nonunique, representations of vectors in a Hilbert space H. The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, and Type II duals have been introduced in the literature because of the special properties that they possess. A Type I dual is a dual such that the range of its synthesis operator is contained in the range of the synthesis operator of the original frame sequence, and a Type II dual is a dual such that the range of its analysis operator is contained in the range of the analysis operator of the original frame sequence. This paper proves that all Type I and Type II duals are oblique duals, but not conversely, and characterizes the existence of oblique and Type II duals in terms of direct sum decompositions of H, as well as characterizing when the Type I, Type II, and oblique duals will be unique. These results are also applied to the case of shift-generated sequences that are frames for shift-invariant subspaces of L2($ ℝ^{d} $). | ||
| 650 | 4 | |a Angle between subspaces |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Frame |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Frame sequence |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Gramian operator |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Oblique dual |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Oblique projection |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Perturbation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Riesz basis |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Type I dual |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Type II dual |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Koo, Yoo Young |e verfasserin |4 aut | |
| 700 | 1 | |a Lim, Jae Kun |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Acta applicandae mathematicae |d [S.l.] : Proquest, 1983 |g 107(2008), 1-3 vom: 16. Dez., Seite 75-90 |w (DE-627)271176105 |w (DE-600)1479016-6 |x 1572-9036 |7 nnns |
| 773 | 1 | 8 | |g volume:107 |g year:2008 |g number:1-3 |g day:16 |g month:12 |g pages:75-90 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s10440-008-9410-4 |z lizenzpflichtig |3 Volltext |
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| 912 | |a GBV_ILN_2021 | ||
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| 912 | |a GBV_ILN_2026 | ||
| 912 | |a GBV_ILN_2027 | ||
| 912 | |a GBV_ILN_2031 | ||
| 912 | |a GBV_ILN_2034 | ||
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| 912 | |a GBV_ILN_2057 | ||
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| 912 | |a GBV_ILN_2061 | ||
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| 912 | |a GBV_ILN_2068 | ||
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| 912 | |a GBV_ILN_2116 | ||
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| 912 | |a GBV_ILN_4251 | ||
| 912 | |a GBV_ILN_4305 | ||
| 912 | |a GBV_ILN_4306 | ||
| 912 | |a GBV_ILN_4307 | ||
| 912 | |a GBV_ILN_4313 | ||
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| 912 | |a GBV_ILN_4338 | ||
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10.1007/s10440-008-9410-4 doi (DE-627)SPR010079173 (SPR)s10440-008-9410-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl Heil, Christopher verfasserin aut Duals of Frame Sequences 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Frames provide unconditional basis-like, but generally nonunique, representations of vectors in a Hilbert space H. The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, and Type II duals have been introduced in the literature because of the special properties that they possess. A Type I dual is a dual such that the range of its synthesis operator is contained in the range of the synthesis operator of the original frame sequence, and a Type II dual is a dual such that the range of its analysis operator is contained in the range of the analysis operator of the original frame sequence. This paper proves that all Type I and Type II duals are oblique duals, but not conversely, and characterizes the existence of oblique and Type II duals in terms of direct sum decompositions of H, as well as characterizing when the Type I, Type II, and oblique duals will be unique. These results are also applied to the case of shift-generated sequences that are frames for shift-invariant subspaces of L2($ ℝ^{d} $). Angle between subspaces (dpeaa)DE-He213 Frame (dpeaa)DE-He213 Frame sequence (dpeaa)DE-He213 Gramian operator (dpeaa)DE-He213 Oblique dual (dpeaa)DE-He213 Oblique projection (dpeaa)DE-He213 Perturbation (dpeaa)DE-He213 Riesz basis (dpeaa)DE-He213 Type I dual (dpeaa)DE-He213 Type II dual (dpeaa)DE-He213 Koo, Yoo Young verfasserin aut Lim, Jae Kun verfasserin aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 107(2008), 1-3 vom: 16. Dez., Seite 75-90 (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:107 year:2008 number:1-3 day:16 month:12 pages:75-90 https://dx.doi.org/10.1007/s10440-008-9410-4 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_206 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 107 2008 1-3 16 12 75-90 |
| spelling |
10.1007/s10440-008-9410-4 doi (DE-627)SPR010079173 (SPR)s10440-008-9410-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl Heil, Christopher verfasserin aut Duals of Frame Sequences 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Frames provide unconditional basis-like, but generally nonunique, representations of vectors in a Hilbert space H. The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, and Type II duals have been introduced in the literature because of the special properties that they possess. A Type I dual is a dual such that the range of its synthesis operator is contained in the range of the synthesis operator of the original frame sequence, and a Type II dual is a dual such that the range of its analysis operator is contained in the range of the analysis operator of the original frame sequence. This paper proves that all Type I and Type II duals are oblique duals, but not conversely, and characterizes the existence of oblique and Type II duals in terms of direct sum decompositions of H, as well as characterizing when the Type I, Type II, and oblique duals will be unique. These results are also applied to the case of shift-generated sequences that are frames for shift-invariant subspaces of L2($ ℝ^{d} $). Angle between subspaces (dpeaa)DE-He213 Frame (dpeaa)DE-He213 Frame sequence (dpeaa)DE-He213 Gramian operator (dpeaa)DE-He213 Oblique dual (dpeaa)DE-He213 Oblique projection (dpeaa)DE-He213 Perturbation (dpeaa)DE-He213 Riesz basis (dpeaa)DE-He213 Type I dual (dpeaa)DE-He213 Type II dual (dpeaa)DE-He213 Koo, Yoo Young verfasserin aut Lim, Jae Kun verfasserin aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 107(2008), 1-3 vom: 16. Dez., Seite 75-90 (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:107 year:2008 number:1-3 day:16 month:12 pages:75-90 https://dx.doi.org/10.1007/s10440-008-9410-4 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_206 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 107 2008 1-3 16 12 75-90 |
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10.1007/s10440-008-9410-4 doi (DE-627)SPR010079173 (SPR)s10440-008-9410-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl Heil, Christopher verfasserin aut Duals of Frame Sequences 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Frames provide unconditional basis-like, but generally nonunique, representations of vectors in a Hilbert space H. The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, and Type II duals have been introduced in the literature because of the special properties that they possess. A Type I dual is a dual such that the range of its synthesis operator is contained in the range of the synthesis operator of the original frame sequence, and a Type II dual is a dual such that the range of its analysis operator is contained in the range of the analysis operator of the original frame sequence. This paper proves that all Type I and Type II duals are oblique duals, but not conversely, and characterizes the existence of oblique and Type II duals in terms of direct sum decompositions of H, as well as characterizing when the Type I, Type II, and oblique duals will be unique. These results are also applied to the case of shift-generated sequences that are frames for shift-invariant subspaces of L2($ ℝ^{d} $). Angle between subspaces (dpeaa)DE-He213 Frame (dpeaa)DE-He213 Frame sequence (dpeaa)DE-He213 Gramian operator (dpeaa)DE-He213 Oblique dual (dpeaa)DE-He213 Oblique projection (dpeaa)DE-He213 Perturbation (dpeaa)DE-He213 Riesz basis (dpeaa)DE-He213 Type I dual (dpeaa)DE-He213 Type II dual (dpeaa)DE-He213 Koo, Yoo Young verfasserin aut Lim, Jae Kun verfasserin aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 107(2008), 1-3 vom: 16. Dez., Seite 75-90 (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:107 year:2008 number:1-3 day:16 month:12 pages:75-90 https://dx.doi.org/10.1007/s10440-008-9410-4 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_206 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 107 2008 1-3 16 12 75-90 |
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10.1007/s10440-008-9410-4 doi (DE-627)SPR010079173 (SPR)s10440-008-9410-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl Heil, Christopher verfasserin aut Duals of Frame Sequences 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Frames provide unconditional basis-like, but generally nonunique, representations of vectors in a Hilbert space H. The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, and Type II duals have been introduced in the literature because of the special properties that they possess. A Type I dual is a dual such that the range of its synthesis operator is contained in the range of the synthesis operator of the original frame sequence, and a Type II dual is a dual such that the range of its analysis operator is contained in the range of the analysis operator of the original frame sequence. This paper proves that all Type I and Type II duals are oblique duals, but not conversely, and characterizes the existence of oblique and Type II duals in terms of direct sum decompositions of H, as well as characterizing when the Type I, Type II, and oblique duals will be unique. These results are also applied to the case of shift-generated sequences that are frames for shift-invariant subspaces of L2($ ℝ^{d} $). Angle between subspaces (dpeaa)DE-He213 Frame (dpeaa)DE-He213 Frame sequence (dpeaa)DE-He213 Gramian operator (dpeaa)DE-He213 Oblique dual (dpeaa)DE-He213 Oblique projection (dpeaa)DE-He213 Perturbation (dpeaa)DE-He213 Riesz basis (dpeaa)DE-He213 Type I dual (dpeaa)DE-He213 Type II dual (dpeaa)DE-He213 Koo, Yoo Young verfasserin aut Lim, Jae Kun verfasserin aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 107(2008), 1-3 vom: 16. Dez., Seite 75-90 (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:107 year:2008 number:1-3 day:16 month:12 pages:75-90 https://dx.doi.org/10.1007/s10440-008-9410-4 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_206 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 107 2008 1-3 16 12 75-90 |
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10.1007/s10440-008-9410-4 doi (DE-627)SPR010079173 (SPR)s10440-008-9410-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.80 bkl Heil, Christopher verfasserin aut Duals of Frame Sequences 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Frames provide unconditional basis-like, but generally nonunique, representations of vectors in a Hilbert space H. The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, and Type II duals have been introduced in the literature because of the special properties that they possess. A Type I dual is a dual such that the range of its synthesis operator is contained in the range of the synthesis operator of the original frame sequence, and a Type II dual is a dual such that the range of its analysis operator is contained in the range of the analysis operator of the original frame sequence. This paper proves that all Type I and Type II duals are oblique duals, but not conversely, and characterizes the existence of oblique and Type II duals in terms of direct sum decompositions of H, as well as characterizing when the Type I, Type II, and oblique duals will be unique. These results are also applied to the case of shift-generated sequences that are frames for shift-invariant subspaces of L2($ ℝ^{d} $). Angle between subspaces (dpeaa)DE-He213 Frame (dpeaa)DE-He213 Frame sequence (dpeaa)DE-He213 Gramian operator (dpeaa)DE-He213 Oblique dual (dpeaa)DE-He213 Oblique projection (dpeaa)DE-He213 Perturbation (dpeaa)DE-He213 Riesz basis (dpeaa)DE-He213 Type I dual (dpeaa)DE-He213 Type II dual (dpeaa)DE-He213 Koo, Yoo Young verfasserin aut Lim, Jae Kun verfasserin aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 107(2008), 1-3 vom: 16. Dez., Seite 75-90 (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:107 year:2008 number:1-3 day:16 month:12 pages:75-90 https://dx.doi.org/10.1007/s10440-008-9410-4 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_206 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 107 2008 1-3 16 12 75-90 |
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Enthalten in Acta applicandae mathematicae 107(2008), 1-3 vom: 16. Dez., Seite 75-90 volume:107 year:2008 number:1-3 day:16 month:12 pages:75-90 |
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Angle between subspaces Frame Frame sequence Gramian operator Oblique dual Oblique projection Perturbation Riesz basis Type I dual Type II dual |
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Heil, Christopher @@aut@@ Koo, Yoo Young @@aut@@ Lim, Jae Kun @@aut@@ |
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The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, and Type II duals have been introduced in the literature because of the special properties that they possess. A Type I dual is a dual such that the range of its synthesis operator is contained in the range of the synthesis operator of the original frame sequence, and a Type II dual is a dual such that the range of its analysis operator is contained in the range of the analysis operator of the original frame sequence. This paper proves that all Type I and Type II duals are oblique duals, but not conversely, and characterizes the existence of oblique and Type II duals in terms of direct sum decompositions of H, as well as characterizing when the Type I, Type II, and oblique duals will be unique. 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510 ASE 31.80 bkl Duals of Frame Sequences Angle between subspaces (dpeaa)DE-He213 Frame (dpeaa)DE-He213 Frame sequence (dpeaa)DE-He213 Gramian operator (dpeaa)DE-He213 Oblique dual (dpeaa)DE-He213 Oblique projection (dpeaa)DE-He213 Perturbation (dpeaa)DE-He213 Riesz basis (dpeaa)DE-He213 Type I dual (dpeaa)DE-He213 Type II dual (dpeaa)DE-He213 |
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Duals of Frame Sequences |
| abstract |
Abstract Frames provide unconditional basis-like, but generally nonunique, representations of vectors in a Hilbert space H. The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, and Type II duals have been introduced in the literature because of the special properties that they possess. A Type I dual is a dual such that the range of its synthesis operator is contained in the range of the synthesis operator of the original frame sequence, and a Type II dual is a dual such that the range of its analysis operator is contained in the range of the analysis operator of the original frame sequence. This paper proves that all Type I and Type II duals are oblique duals, but not conversely, and characterizes the existence of oblique and Type II duals in terms of direct sum decompositions of H, as well as characterizing when the Type I, Type II, and oblique duals will be unique. These results are also applied to the case of shift-generated sequences that are frames for shift-invariant subspaces of L2($ ℝ^{d} $). |
| abstractGer |
Abstract Frames provide unconditional basis-like, but generally nonunique, representations of vectors in a Hilbert space H. The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, and Type II duals have been introduced in the literature because of the special properties that they possess. A Type I dual is a dual such that the range of its synthesis operator is contained in the range of the synthesis operator of the original frame sequence, and a Type II dual is a dual such that the range of its analysis operator is contained in the range of the analysis operator of the original frame sequence. This paper proves that all Type I and Type II duals are oblique duals, but not conversely, and characterizes the existence of oblique and Type II duals in terms of direct sum decompositions of H, as well as characterizing when the Type I, Type II, and oblique duals will be unique. These results are also applied to the case of shift-generated sequences that are frames for shift-invariant subspaces of L2($ ℝ^{d} $). |
| abstract_unstemmed |
Abstract Frames provide unconditional basis-like, but generally nonunique, representations of vectors in a Hilbert space H. The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, and Type II duals have been introduced in the literature because of the special properties that they possess. A Type I dual is a dual such that the range of its synthesis operator is contained in the range of the synthesis operator of the original frame sequence, and a Type II dual is a dual such that the range of its analysis operator is contained in the range of the analysis operator of the original frame sequence. This paper proves that all Type I and Type II duals are oblique duals, but not conversely, and characterizes the existence of oblique and Type II duals in terms of direct sum decompositions of H, as well as characterizing when the Type I, Type II, and oblique duals will be unique. These results are also applied to the case of shift-generated sequences that are frames for shift-invariant subspaces of L2($ ℝ^{d} $). |
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| container_issue |
1-3 |
| title_short |
Duals of Frame Sequences |
| url |
https://dx.doi.org/10.1007/s10440-008-9410-4 |
| remote_bool |
true |
| author2 |
Koo, Yoo Young Lim, Jae Kun |
| author2Str |
Koo, Yoo Young Lim, Jae Kun |
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271176105 |
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c |
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| hochschulschrift_bool |
false |
| doi_str |
10.1007/s10440-008-9410-4 |
| up_date |
2024-07-03T13:49:33.946Z |
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| score |
7.3988647 |