Minimal Frame Operator Norms Via Minimal Theta Functions

We investigate sharp frame bounds of Gabor frames with chirped Gaussians and rectangular lattices or, equivalently, the case of the standard Gaussian and general lattices. We prove that for even redundancy and standard Gaussian window the hexagonal lattice minimizes the upper frame bound using a res...

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Detalles Bibliográficos
Autor principal: Faulhuber, Markus
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2017
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935039/
https://www.ncbi.nlm.nih.gov/pubmed/29755253
http://dx.doi.org/10.1007/s00041-017-9526-x
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author Faulhuber, Markus
author_facet Faulhuber, Markus
author_sort Faulhuber, Markus
collection PubMed
description We investigate sharp frame bounds of Gabor frames with chirped Gaussians and rectangular lattices or, equivalently, the case of the standard Gaussian and general lattices. We prove that for even redundancy and standard Gaussian window the hexagonal lattice minimizes the upper frame bound using a result by Montgomery on minimal theta functions.
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spelling pubmed-59350392018-05-09 Minimal Frame Operator Norms Via Minimal Theta Functions Faulhuber, Markus J Fourier Anal Appl Article We investigate sharp frame bounds of Gabor frames with chirped Gaussians and rectangular lattices or, equivalently, the case of the standard Gaussian and general lattices. We prove that for even redundancy and standard Gaussian window the hexagonal lattice minimizes the upper frame bound using a result by Montgomery on minimal theta functions. Springer US 2017-02-11 2018 /pmc/articles/PMC5935039/ /pubmed/29755253 http://dx.doi.org/10.1007/s00041-017-9526-x Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Faulhuber, Markus
Minimal Frame Operator Norms Via Minimal Theta Functions
title Minimal Frame Operator Norms Via Minimal Theta Functions
title_full Minimal Frame Operator Norms Via Minimal Theta Functions
title_fullStr Minimal Frame Operator Norms Via Minimal Theta Functions
title_full_unstemmed Minimal Frame Operator Norms Via Minimal Theta Functions
title_short Minimal Frame Operator Norms Via Minimal Theta Functions
title_sort minimal frame operator norms via minimal theta functions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935039/
https://www.ncbi.nlm.nih.gov/pubmed/29755253
http://dx.doi.org/10.1007/s00041-017-9526-x
work_keys_str_mv AT faulhubermarkus minimalframeoperatornormsviaminimalthetafunctions

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