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Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 469341, 12 pages
http://dx.doi.org/10.1155/2012/469341
Research Article

Reproducing Kernels and Variable Bandwidth

1Faculty of Mechanical Engineering, Ss. Cyril and Methodius University, Karposh II b.b., 1000 Skopje, Macedonia
2Faculty of Mathematics, NuHAG, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austria

Received 20 June 2012; Accepted 27 August 2012

Academic Editor: Baoxiang Wang

Copyright © 2012 R. Aceska and H. G. Feichtinger. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.