Frames of translates with prescribed fine structure in shift invariant spaces

Autores
Benac, Maria Jose; Massey, Pedro Gustavo; Stojanoff, Demetrio
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
For a given finitely generated shift invariant (FSI) subspace W⊂L2(Rk) we obtain a simple criterion for the existence of shift generated (SG) Bessel sequences E(F) induced by finite sequences of vectors F∈Wn that have a prescribed fine structure i.e., such that the norms of the vectors in F and the spectra of SE(F) are prescribed in each fiber of Spec(W)⊂Tk. We complement this result by developing an analogue of the so-called sequences of eigensteps from finite frame theory in the context of SG Bessel sequences, that allows for a detailed description of all sequences with prescribed fine structure. Then, given α1≥…≥αn>0 we characterize the finite sequences F∈Wn such that ‖fi‖2=αi, for 1≤i≤n, and such that the fine spectral structure of the shift generated Bessel sequences E(F) has minimal spread (i.e. we show the existence of optimal SG Bessel sequences with prescribed norms); in this context the spread of the spectra is measured in terms of the convex potential Pφ W induced by W and an arbitrary convex function φ:R+→R+.
Fil: Benac, Maria Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
CONVEX POTENTIALS
FRAME DESIGN PROBLEMS
FRAMES OF TRANSLATES
SHIFT INVARIANT SUBSPACES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/38716
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/38716
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Frames of translates with prescribed fine structure in shift invariant spacesBenac, Maria JoseMassey, Pedro GustavoStojanoff, DemetrioCONVEX POTENTIALSFRAME DESIGN PROBLEMSFRAMES OF TRANSLATESSHIFT INVARIANT SUBSPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1For a given finitely generated shift invariant (FSI) subspace W⊂L2(Rk) we obtain a simple criterion for the existence of shift generated (SG) Bessel sequences E(F) induced by finite sequences of vectors F∈Wn that have a prescribed fine structure i.e., such that the norms of the vectors in F and the spectra of SE(F) are prescribed in each fiber of Spec(W)⊂Tk. We complement this result by developing an analogue of the so-called sequences of eigensteps from finite frame theory in the context of SG Bessel sequences, that allows for a detailed description of all sequences with prescribed fine structure. Then, given α1≥…≥αn>0 we characterize the finite sequences F∈Wn such that ‖fi‖2=αi, for 1≤i≤n, and such that the fine spectral structure of the shift generated Bessel sequences E(F) has minimal spread (i.e. we show the existence of optimal SG Bessel sequences with prescribed norms); in this context the spread of the spectra is measured in terms of the convex potential Pφ W induced by W and an arbitrary convex function φ:R+→R+.Fil: Benac, Maria Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaAcademic Press Inc Elsevier Science2016-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/38716Benac, Maria Jose; Massey, Pedro Gustavo; Stojanoff, Demetrio; Frames of translates with prescribed fine structure in shift invariant spaces; Academic Press Inc Elsevier Science; Journal Of Functional Analysis; 271; 9; 11-2016; 2631-26710022-1236CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2016.07.007info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022123616301951info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:51:08Zoai:ri.conicet.gov.ar:11336/38716instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:51:09.033CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Frames of translates with prescribed fine structure in shift invariant spaces
title Frames of translates with prescribed fine structure in shift invariant spaces
spellingShingle Frames of translates with prescribed fine structure in shift invariant spaces
Benac, Maria Jose
CONVEX POTENTIALS
FRAME DESIGN PROBLEMS
FRAMES OF TRANSLATES
SHIFT INVARIANT SUBSPACES
title_short Frames of translates with prescribed fine structure in shift invariant spaces
title_full Frames of translates with prescribed fine structure in shift invariant spaces
title_fullStr Frames of translates with prescribed fine structure in shift invariant spaces
title_full_unstemmed Frames of translates with prescribed fine structure in shift invariant spaces
title_sort Frames of translates with prescribed fine structure in shift invariant spaces
dc.creator.none.fl_str_mv Benac, Maria Jose
Massey, Pedro Gustavo
Stojanoff, Demetrio
author Benac, Maria Jose
author_facet Benac, Maria Jose
Massey, Pedro Gustavo
Stojanoff, Demetrio
author_role author
author2 Massey, Pedro Gustavo
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv CONVEX POTENTIALS
FRAME DESIGN PROBLEMS
FRAMES OF TRANSLATES
SHIFT INVARIANT SUBSPACES
topic CONVEX POTENTIALS
FRAME DESIGN PROBLEMS
FRAMES OF TRANSLATES
SHIFT INVARIANT SUBSPACES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv For a given finitely generated shift invariant (FSI) subspace W⊂L2(Rk) we obtain a simple criterion for the existence of shift generated (SG) Bessel sequences E(F) induced by finite sequences of vectors F∈Wn that have a prescribed fine structure i.e., such that the norms of the vectors in F and the spectra of SE(F) are prescribed in each fiber of Spec(W)⊂Tk. We complement this result by developing an analogue of the so-called sequences of eigensteps from finite frame theory in the context of SG Bessel sequences, that allows for a detailed description of all sequences with prescribed fine structure. Then, given α1≥…≥αn>0 we characterize the finite sequences F∈Wn such that ‖fi‖2=αi, for 1≤i≤n, and such that the fine spectral structure of the shift generated Bessel sequences E(F) has minimal spread (i.e. we show the existence of optimal SG Bessel sequences with prescribed norms); in this context the spread of the spectra is measured in terms of the convex potential Pφ W induced by W and an arbitrary convex function φ:R+→R+.
Fil: Benac, Maria Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description For a given finitely generated shift invariant (FSI) subspace W⊂L2(Rk) we obtain a simple criterion for the existence of shift generated (SG) Bessel sequences E(F) induced by finite sequences of vectors F∈Wn that have a prescribed fine structure i.e., such that the norms of the vectors in F and the spectra of SE(F) are prescribed in each fiber of Spec(W)⊂Tk. We complement this result by developing an analogue of the so-called sequences of eigensteps from finite frame theory in the context of SG Bessel sequences, that allows for a detailed description of all sequences with prescribed fine structure. Then, given α1≥…≥αn>0 we characterize the finite sequences F∈Wn such that ‖fi‖2=αi, for 1≤i≤n, and such that the fine spectral structure of the shift generated Bessel sequences E(F) has minimal spread (i.e. we show the existence of optimal SG Bessel sequences with prescribed norms); in this context the spread of the spectra is measured in terms of the convex potential Pφ W induced by W and an arbitrary convex function φ:R+→R+.
publishDate 2016
dc.date.none.fl_str_mv 2016-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/38716
Benac, Maria Jose; Massey, Pedro Gustavo; Stojanoff, Demetrio; Frames of translates with prescribed fine structure in shift invariant spaces; Academic Press Inc Elsevier Science; Journal Of Functional Analysis; 271; 9; 11-2016; 2631-2671
0022-1236
CONICET Digital
CONICET
url http://hdl.handle.net/11336/38716
identifier_str_mv Benac, Maria Jose; Massey, Pedro Gustavo; Stojanoff, Demetrio; Frames of translates with prescribed fine structure in shift invariant spaces; Academic Press Inc Elsevier Science; Journal Of Functional Analysis; 271; 9; 11-2016; 2631-2671
0022-1236
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2016.07.007
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022123616301951
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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