Critical pairs of sequences of a mixed frame potential

The classical frame potential in a finite-dimensional Hilbert space has been introduced by Benedetto and Fickus, who showed that all finite unit-norm tight frames can be characterized as the minimizers of this energy functional. This was the starting point of a series of new results in frame theory,...

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Detalles Bibliográficos
Autor principal: Heineken, Sigrid Bettina
Publicado: 2014
Materias:
Dual frames
Finite frames
Frame potential
Lagrange multipliers
Functional analysis
Mathematical techniques
Energy functionals
Frame theory
Fusion frames
New results
Restricted-domain
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01630563_v35_n6_p665_Carrizo
http://hdl.handle.net/20.500.12110/paper_01630563_v35_n6_p665_Carrizo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_01630563_v35_n6_p665_Carrizo
record_format dspace
spelling paper:paper_01630563_v35_n6_p665_Carrizo2023-06-08T15:13:42Z Critical pairs of sequences of a mixed frame potential Heineken, Sigrid Bettina Dual frames Finite frames Frame potential Lagrange multipliers Functional analysis Mathematical techniques Dual frames Energy functionals Finite frames Frame potential Frame theory Fusion frames New results Restricted-domain Lagrange multipliers The classical frame potential in a finite-dimensional Hilbert space has been introduced by Benedetto and Fickus, who showed that all finite unit-norm tight frames can be characterized as the minimizers of this energy functional. This was the starting point of a series of new results in frame theory, related to finding tight frames with determined lengths. The frame potential has been studied in the traditional setting as well as in the finite-dimensional fusion frame context. In this work we introduce the concept of mixed frame potential, which generalizes the notion of the Benedetto-Fickus frame potential. We study properties of this new potential, and give the structure of its critical pairs of sequences on a suitable restricted domain. For a given sequence {m } m=1.. N in K, where K is or , we obtain necessary and sufficient conditions in order to have a dual pair of frames {f m m=1. N, {g m } m=1.. N such that f m, g m = m for all m = 1.. N. copy; 2014 Copyright Taylor & Francis Group, LLC. Fil:Heineken, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01630563_v35_n6_p665_Carrizo http://hdl.handle.net/20.500.12110/paper_01630563_v35_n6_p665_Carrizo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Dual frames
Finite frames
Frame potential
Lagrange multipliers
Functional analysis
Mathematical techniques
Dual frames
Energy functionals
Finite frames
Frame potential
Frame theory
Fusion frames
New results
Restricted-domain
Lagrange multipliers
spellingShingle Dual frames
Finite frames
Frame potential
Lagrange multipliers
Functional analysis
Mathematical techniques
Dual frames
Energy functionals
Finite frames
Frame potential
Frame theory
Fusion frames
New results
Restricted-domain
Lagrange multipliers
Heineken, Sigrid Bettina
Critical pairs of sequences of a mixed frame potential
topic_facet Dual frames
Finite frames
Frame potential
Lagrange multipliers
Functional analysis
Mathematical techniques
Dual frames
Energy functionals
Finite frames
Frame potential
Frame theory
Fusion frames
New results
Restricted-domain
Lagrange multipliers
description The classical frame potential in a finite-dimensional Hilbert space has been introduced by Benedetto and Fickus, who showed that all finite unit-norm tight frames can be characterized as the minimizers of this energy functional. This was the starting point of a series of new results in frame theory, related to finding tight frames with determined lengths. The frame potential has been studied in the traditional setting as well as in the finite-dimensional fusion frame context. In this work we introduce the concept of mixed frame potential, which generalizes the notion of the Benedetto-Fickus frame potential. We study properties of this new potential, and give the structure of its critical pairs of sequences on a suitable restricted domain. For a given sequence {m } m=1.. N in K, where K is or , we obtain necessary and sufficient conditions in order to have a dual pair of frames {f m m=1. N, {g m } m=1.. N such that f m, g m = m for all m = 1.. N. copy; 2014 Copyright Taylor & Francis Group, LLC.
author Heineken, Sigrid Bettina
author_facet Heineken, Sigrid Bettina
author_sort Heineken, Sigrid Bettina
title Critical pairs of sequences of a mixed frame potential
title_short Critical pairs of sequences of a mixed frame potential
title_full Critical pairs of sequences of a mixed frame potential
title_fullStr Critical pairs of sequences of a mixed frame potential
title_full_unstemmed Critical pairs of sequences of a mixed frame potential
title_sort critical pairs of sequences of a mixed frame potential
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01630563_v35_n6_p665_Carrizo
http://hdl.handle.net/20.500.12110/paper_01630563_v35_n6_p665_Carrizo
work_keys_str_mv AT heinekensigridbettina criticalpairsofsequencesofamixedframepotential
_version_ 1768545368543330304

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