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- Title
Gabor Analysis on Wiener Amalgams.
- Authors
Feichtinger, Hans G.; Weisz, Ferenc
- Abstract
A general summability method, the so-called θ-summability, is considered for Gabor series. Under suitable conditions on θ we prove that this summation method of the Gabor expansion of f converges to f in Wiener amalgam norms, and in particular with respect to [Lp-norms, for functions f from the corresponding spaces, as well as almost everywhere. Some inequalities for the maximal operator of the θ-means of the Gabor expansion are obtained. The analogous statements for the partial sums of Gabor series are also given. The classical Hardy-Littlewood inequality and the Marcinkiewicz multiplier theorem is shown to be valid in the context of Gabor series.
- Subjects
SUMMABILITY theory; PARTIAL sums (Series); HARDY-Littlewood method; TIME series analysis; MULTIPLIERS (Mathematical analysis); MATHEMATICAL series
- Publication
Sampling Theory in Signal & Image Processing, 2007, Vol 6, Issue 2, p129
- ISSN
1530-6429
- Publication type
Article
- DOI
10.1007/bf03549468