Bessel orbits of normal operators

Given a bounded normal operator A in a Hilbert space and a fixed vector x, we elaborate on the problem of finding necessary and sufficient conditions under which (Akx)k∈N constitutes a Bessel sequence. We provide a characterization in terms of the measure ‖E(⋅)x‖2, where E is the spectral measure of...

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Autor principal: Philipp, F.
Formato: JOUR
Materias:
Bessel sequence
Dynamical sampling
Hankel matrix
Hardy space
Toeplitz matrix
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v448_n2_p767_Philipp
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_0022247X_v448_n2_p767_Philipp
record_format dspace
spelling todo:paper_0022247X_v448_n2_p767_Philipp2023-10-03T14:29:23Z Bessel orbits of normal operators Philipp, F. Bessel sequence Dynamical sampling Hankel matrix Hardy space Toeplitz matrix Given a bounded normal operator A in a Hilbert space and a fixed vector x, we elaborate on the problem of finding necessary and sufficient conditions under which (Akx)k∈N constitutes a Bessel sequence. We provide a characterization in terms of the measure ‖E(⋅)x‖2, where E is the spectral measure of the operator A. In the separately treated special cases where A is unitary or selfadjoint we obtain more explicit characterizations. Finally, we apply our results to a sequence (Akx)k∈N, where A arises from the heat equation. The problem is motivated by and related to the new field of Dynamical Sampling which was recently initiated by Aldroubi et al. in [3]. © 2016 Elsevier Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v448_n2_p767_Philipp
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Bessel sequence
Dynamical sampling
Hankel matrix
Hardy space
Toeplitz matrix
spellingShingle Bessel sequence
Dynamical sampling
Hankel matrix
Hardy space
Toeplitz matrix
Philipp, F.
Bessel orbits of normal operators
topic_facet Bessel sequence
Dynamical sampling
Hankel matrix
Hardy space
Toeplitz matrix
description Given a bounded normal operator A in a Hilbert space and a fixed vector x, we elaborate on the problem of finding necessary and sufficient conditions under which (Akx)k∈N constitutes a Bessel sequence. We provide a characterization in terms of the measure ‖E(⋅)x‖2, where E is the spectral measure of the operator A. In the separately treated special cases where A is unitary or selfadjoint we obtain more explicit characterizations. Finally, we apply our results to a sequence (Akx)k∈N, where A arises from the heat equation. The problem is motivated by and related to the new field of Dynamical Sampling which was recently initiated by Aldroubi et al. in [3]. © 2016 Elsevier Inc.
format JOUR
author Philipp, F.
author_facet Philipp, F.
author_sort Philipp, F.
title Bessel orbits of normal operators
title_short Bessel orbits of normal operators
title_full Bessel orbits of normal operators
title_fullStr Bessel orbits of normal operators
title_full_unstemmed Bessel orbits of normal operators
title_sort bessel orbits of normal operators
url http://hdl.handle.net/20.500.12110/paper_0022247X_v448_n2_p767_Philipp
work_keys_str_mv AT philippf besselorbitsofnormaloperators
_version_ 1807315258613694464

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