Reproducing Kernels and Variable Bandwidth

Reproducing Kernels and Variable Bandwidth

We show that a modulation space of type () is a reproducing kernel Hilbert space (RKHS). In particular, we explore the special cases of variable bandwidth spaces Aceska and Feichtinger (2011) with a suitably chosen weight to provide strong enough decay in the frequency direction. The reproducing ke...

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Bibliographic Details
Main Authors: R. Aceska, H. G. Feichtinger
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2012/469341
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spelling doaj-1c4c7beae3984325aecd2027429f24192020-11-24T22:50:15ZengHindawi LimitedJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/469341469341Reproducing Kernels and Variable BandwidthR. Aceska0H. G. Feichtinger1Faculty of Mechanical Engineering, Ss. Cyril and Methodius University, Karposh II b.b., 1000 Skopje, MacedoniaFaculty of Mathematics, NuHAG, University of Vienna, Nordbergstrasse 15, 1090 Vienna, AustriaWe show that a modulation space of type () is a reproducing kernel Hilbert space (RKHS). In particular, we explore the special cases of variable bandwidth spaces Aceska and Feichtinger (2011) with a suitably chosen weight to provide strong enough decay in the frequency direction. The reproducing kernel property is valid even if () does not coincide with any of the classical Sobolev spaces because unbounded bandwidth (globally) is allowed. The reproducing kernel will be described explicitly.http://dx.doi.org/10.1155/2012/469341
collection DOAJ
language English
format Article
sources DOAJ
author R. Aceska
H. G. Feichtinger
spellingShingle R. Aceska
H. G. Feichtinger
Reproducing Kernels and Variable Bandwidth
Journal of Function Spaces and Applications
author_facet R. Aceska
H. G. Feichtinger
author_sort R. Aceska
title Reproducing Kernels and Variable Bandwidth
title_short Reproducing Kernels and Variable Bandwidth
title_full Reproducing Kernels and Variable Bandwidth
title_fullStr Reproducing Kernels and Variable Bandwidth
title_full_unstemmed Reproducing Kernels and Variable Bandwidth
title_sort reproducing kernels and variable bandwidth
publisher Hindawi Limited
series Journal of Function Spaces and Applications
issn 0972-6802
1758-4965
publishDate 2012-01-01
description We show that a modulation space of type () is a reproducing kernel Hilbert space (RKHS). In particular, we explore the special cases of variable bandwidth spaces Aceska and Feichtinger (2011) with a suitably chosen weight to provide strong enough decay in the frequency direction. The reproducing kernel property is valid even if () does not coincide with any of the classical Sobolev spaces because unbounded bandwidth (globally) is allowed. The reproducing kernel will be described explicitly.
url http://dx.doi.org/10.1155/2012/469341
work_keys_str_mv AT raceska reproducingkernelsandvariablebandwidth
AT hgfeichtinger reproducingkernelsandvariablebandwidth
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