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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/38716
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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 Técnicas2025-09-29T10:18:25Zoai: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:34982025-09-29 10:18:25.659CONICET 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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1844614145956118528 |
score |
13.070432 |