Bimodal Wilson systems in

Given a window ϕ ∈ L 2 ( R ) , and...
Ausführliche Beschreibung

Given a window ϕ ∈ L 2 ( R ) , and lattice parameters α , β > 0 , we introduce a bimodal Wilson system W ( ϕ , α , β ) consisting of linear combinations of at most two elements from an associated Gabor G ( ϕ , α , β ) . For a class of window functions ϕ, we show that the Gabor system G ( ϕ , α , β ) is a tight frame of redundancy β − 1 if and only if the Wilson system W ( ϕ , α , β ) is Parseval system for L 2 ( R ) . Examples of smooth rapidly decaying generators ϕ are constructed. In addition, when 3 ≤ β − 1 ∈ N , we prove that it is impossible to renormalize the elements of the constructed Parseval Wilson frame so as to get a well-localized orthonormal basis for L 2 ( R ) . Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Bhimani, Divyang G. [verfasserIn] Okoudjou, Kasso A. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Frame Gabor system Orthonormal basis Wilson system

Übergeordnetes Werk:	Enthalten in: Journal of mathematical analysis and applications - Amsterdam [u.a.] : Elsevier, 1960, 505
Übergeordnetes Werk:	volume:505

DOI / URN:	10.1016/j.jmaa.2021.125480

Katalog-ID:	ELV006654754

Internformat


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520			\|a Given a window ϕ ∈ L 2 ( R ) , and lattice parameters α , β > 0 , we introduce a bimodal Wilson system W ( ϕ , α , β ) consisting of linear combinations of at most two elements from an associated Gabor G ( ϕ , α , β ) . For a class of window functions ϕ, we show that the Gabor system G ( ϕ , α , β ) is a tight frame of redundancy β − 1 if and only if the Wilson system W ( ϕ , α , β ) is Parseval system for L 2 ( R ) . Examples of smooth rapidly decaying generators ϕ are constructed. In addition, when 3 ≤ β − 1 ∈ N , we prove that it is impossible to renormalize the elements of the constructed Parseval Wilson frame so as to get a well-localized orthonormal basis for L 2 ( R ) .
650		4	\|a Frame
650		4	\|a Gabor system
650		4	\|a Orthonormal basis
650		4	\|a Wilson system
700	1		\|a Okoudjou, Kasso A. \|e verfasserin \|0 (orcid)0000-0003-4679-5534 \|4 aut
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912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_224
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
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
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
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936	b	k	\|a 31.00 \|j Mathematik: Allgemeines
951			\|a AR
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author_variant	d g b dg dgb k a o ka kao
matchkey_str	article:10960813:2021----::ioawlos
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bklnumber	31.00
publishDate	2021
allfields	10.1016/j.jmaa.2021.125480 doi (DE-627)ELV006654754 (ELSEVIER)S0022-247X(21)00559-X DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Bhimani, Divyang G. verfasserin aut Bimodal Wilson systems in 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Given a window ϕ ∈ L 2 ( R ) , and lattice parameters α , β > 0 , we introduce a bimodal Wilson system W ( ϕ , α , β ) consisting of linear combinations of at most two elements from an associated Gabor G ( ϕ , α , β ) . For a class of window functions ϕ, we show that the Gabor system G ( ϕ , α , β ) is a tight frame of redundancy β − 1 if and only if the Wilson system W ( ϕ , α , β ) is Parseval system for L 2 ( R ) . Examples of smooth rapidly decaying generators ϕ are constructed. In addition, when 3 ≤ β − 1 ∈ N , we prove that it is impossible to renormalize the elements of the constructed Parseval Wilson frame so as to get a well-localized orthonormal basis for L 2 ( R ) . Frame Gabor system Orthonormal basis Wilson system Okoudjou, Kasso A. verfasserin (orcid)0000-0003-4679-5534 aut Enthalten in Journal of mathematical analysis and applications Amsterdam [u.a.] : Elsevier, 1960 505 Online-Ressource (DE-627)266886922 (DE-600)1468566-8 (DE-576)103373101 1096-0813 nnns volume:505 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 505
spelling	10.1016/j.jmaa.2021.125480 doi (DE-627)ELV006654754 (ELSEVIER)S0022-247X(21)00559-X DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Bhimani, Divyang G. verfasserin aut Bimodal Wilson systems in 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Given a window ϕ ∈ L 2 ( R ) , and lattice parameters α , β > 0 , we introduce a bimodal Wilson system W ( ϕ , α , β ) consisting of linear combinations of at most two elements from an associated Gabor G ( ϕ , α , β ) . For a class of window functions ϕ, we show that the Gabor system G ( ϕ , α , β ) is a tight frame of redundancy β − 1 if and only if the Wilson system W ( ϕ , α , β ) is Parseval system for L 2 ( R ) . Examples of smooth rapidly decaying generators ϕ are constructed. In addition, when 3 ≤ β − 1 ∈ N , we prove that it is impossible to renormalize the elements of the constructed Parseval Wilson frame so as to get a well-localized orthonormal basis for L 2 ( R ) . Frame Gabor system Orthonormal basis Wilson system Okoudjou, Kasso A. verfasserin (orcid)0000-0003-4679-5534 aut Enthalten in Journal of mathematical analysis and applications Amsterdam [u.a.] : Elsevier, 1960 505 Online-Ressource (DE-627)266886922 (DE-600)1468566-8 (DE-576)103373101 1096-0813 nnns volume:505 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 505
allfields_unstemmed	10.1016/j.jmaa.2021.125480 doi (DE-627)ELV006654754 (ELSEVIER)S0022-247X(21)00559-X DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Bhimani, Divyang G. verfasserin aut Bimodal Wilson systems in 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Given a window ϕ ∈ L 2 ( R ) , and lattice parameters α , β > 0 , we introduce a bimodal Wilson system W ( ϕ , α , β ) consisting of linear combinations of at most two elements from an associated Gabor G ( ϕ , α , β ) . For a class of window functions ϕ, we show that the Gabor system G ( ϕ , α , β ) is a tight frame of redundancy β − 1 if and only if the Wilson system W ( ϕ , α , β ) is Parseval system for L 2 ( R ) . Examples of smooth rapidly decaying generators ϕ are constructed. In addition, when 3 ≤ β − 1 ∈ N , we prove that it is impossible to renormalize the elements of the constructed Parseval Wilson frame so as to get a well-localized orthonormal basis for L 2 ( R ) . Frame Gabor system Orthonormal basis Wilson system Okoudjou, Kasso A. verfasserin (orcid)0000-0003-4679-5534 aut Enthalten in Journal of mathematical analysis and applications Amsterdam [u.a.] : Elsevier, 1960 505 Online-Ressource (DE-627)266886922 (DE-600)1468566-8 (DE-576)103373101 1096-0813 nnns volume:505 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 505
allfieldsGer	10.1016/j.jmaa.2021.125480 doi (DE-627)ELV006654754 (ELSEVIER)S0022-247X(21)00559-X DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Bhimani, Divyang G. verfasserin aut Bimodal Wilson systems in 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Given a window ϕ ∈ L 2 ( R ) , and lattice parameters α , β > 0 , we introduce a bimodal Wilson system W ( ϕ , α , β ) consisting of linear combinations of at most two elements from an associated Gabor G ( ϕ , α , β ) . For a class of window functions ϕ, we show that the Gabor system G ( ϕ , α , β ) is a tight frame of redundancy β − 1 if and only if the Wilson system W ( ϕ , α , β ) is Parseval system for L 2 ( R ) . Examples of smooth rapidly decaying generators ϕ are constructed. In addition, when 3 ≤ β − 1 ∈ N , we prove that it is impossible to renormalize the elements of the constructed Parseval Wilson frame so as to get a well-localized orthonormal basis for L 2 ( R ) . Frame Gabor system Orthonormal basis Wilson system Okoudjou, Kasso A. verfasserin (orcid)0000-0003-4679-5534 aut Enthalten in Journal of mathematical analysis and applications Amsterdam [u.a.] : Elsevier, 1960 505 Online-Ressource (DE-627)266886922 (DE-600)1468566-8 (DE-576)103373101 1096-0813 nnns volume:505 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 505
allfieldsSound	10.1016/j.jmaa.2021.125480 doi (DE-627)ELV006654754 (ELSEVIER)S0022-247X(21)00559-X DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Bhimani, Divyang G. verfasserin aut Bimodal Wilson systems in 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Given a window ϕ ∈ L 2 ( R ) , and lattice parameters α , β > 0 , we introduce a bimodal Wilson system W ( ϕ , α , β ) consisting of linear combinations of at most two elements from an associated Gabor G ( ϕ , α , β ) . For a class of window functions ϕ, we show that the Gabor system G ( ϕ , α , β ) is a tight frame of redundancy β − 1 if and only if the Wilson system W ( ϕ , α , β ) is Parseval system for L 2 ( R ) . Examples of smooth rapidly decaying generators ϕ are constructed. In addition, when 3 ≤ β − 1 ∈ N , we prove that it is impossible to renormalize the elements of the constructed Parseval Wilson frame so as to get a well-localized orthonormal basis for L 2 ( R ) . Frame Gabor system Orthonormal basis Wilson system Okoudjou, Kasso A. verfasserin (orcid)0000-0003-4679-5534 aut Enthalten in Journal of mathematical analysis and applications Amsterdam [u.a.] : Elsevier, 1960 505 Online-Ressource (DE-627)266886922 (DE-600)1468566-8 (DE-576)103373101 1096-0813 nnns volume:505 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 505
language	English
source	Enthalten in Journal of mathematical analysis and applications 505 volume:505
sourceStr	Enthalten in Journal of mathematical analysis and applications 505 volume:505
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title_sort	bimodal wilson systems in
title_auth	Bimodal Wilson systems in
abstract	Given a window ϕ ∈ L 2 ( R ) , and lattice parameters α , β > 0 , we introduce a bimodal Wilson system W ( ϕ , α , β ) consisting of linear combinations of at most two elements from an associated Gabor G ( ϕ , α , β ) . For a class of window functions ϕ, we show that the Gabor system G ( ϕ , α , β ) is a tight frame of redundancy β − 1 if and only if the Wilson system W ( ϕ , α , β ) is Parseval system for L 2 ( R ) . Examples of smooth rapidly decaying generators ϕ are constructed. In addition, when 3 ≤ β − 1 ∈ N , we prove that it is impossible to renormalize the elements of the constructed Parseval Wilson frame so as to get a well-localized orthonormal basis for L 2 ( R ) .
abstractGer	Given a window ϕ ∈ L 2 ( R ) , and lattice parameters α , β > 0 , we introduce a bimodal Wilson system W ( ϕ , α , β ) consisting of linear combinations of at most two elements from an associated Gabor G ( ϕ , α , β ) . For a class of window functions ϕ, we show that the Gabor system G ( ϕ , α , β ) is a tight frame of redundancy β − 1 if and only if the Wilson system W ( ϕ , α , β ) is Parseval system for L 2 ( R ) . Examples of smooth rapidly decaying generators ϕ are constructed. In addition, when 3 ≤ β − 1 ∈ N , we prove that it is impossible to renormalize the elements of the constructed Parseval Wilson frame so as to get a well-localized orthonormal basis for L 2 ( R ) .
abstract_unstemmed	Given a window ϕ ∈ L 2 ( R ) , and lattice parameters α , β > 0 , we introduce a bimodal Wilson system W ( ϕ , α , β ) consisting of linear combinations of at most two elements from an associated Gabor G ( ϕ , α , β ) . For a class of window functions ϕ, we show that the Gabor system G ( ϕ , α , β ) is a tight frame of redundancy β − 1 if and only if the Wilson system W ( ϕ , α , β ) is Parseval system for L 2 ( R ) . Examples of smooth rapidly decaying generators ϕ are constructed. In addition, when 3 ≤ β − 1 ∈ N , we prove that it is impossible to renormalize the elements of the constructed Parseval Wilson frame so as to get a well-localized orthonormal basis for L 2 ( R ) .
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title_short	Bimodal Wilson systems in
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In addition, when 3 ≤ β − 1 ∈ N , we prove that it is impossible to renormalize the elements of the constructed Parseval Wilson frame so as to get a well-localized orthonormal basis for L 2 ( R ) .</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Frame</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gabor system</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Orthonormal basis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Wilson system</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Okoudjou, Kasso A.</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-4679-5534</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of mathematical analysis and applications</subfield><subfield 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