Dual pairs of gabor frames for trigonometric generators without the partition of  unity property

Ole Christensen; Mads Sielemann Jakobsen

doi:10.1142/S1793557111000460

Dual pairs of gabor frames for trigonometric generators without the partition of unity property

Ole Christensen, Mads Sielemann Jakobsen

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Abstract

Frames is a strong tool to obtain series expansions in Hilbert spaces under less restrictive conditions than imposed by orthonormal bases. In order to apply frame theory it is necessary to construct a pair of so called dual frames. The goal of the article is to provide explicit constructions of dual pairs of frames having Gabor structure. Unlike the results presented in the literature we do not base the constructions on a generator satisfying the partition of unity constraint.

Translated title of the contribution	DUAL PAIRS OF GABOR FRAMES FOR TRIGONOMETRIC GENERATORS WITHOUT THE PARTITION OF UNITY PROPERTY
Original language	English
Journal	Asian-European Journal of Mathematics
Volume	4
Issue number	4
Pages (from-to)	589–603
ISSN	1793-5571
DOIs	https://doi.org/10.1142/S1793557111000460
Publication status	Published - 2011

Keywords

Gabor frames
dual frame

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10.1142/S1793557111000460

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AB - Frames is a strong tool to obtain series expansions in Hilbert spaces under less restrictive conditions than imposed by orthonormal bases. In order to apply frame theory it is necessary to construct a pair of so called dual frames. The goal of the article is to provide explicit constructions of dual pairs of frames having Gabor structure. Unlike the results presented in the literature we do not base the constructions on a generator satisfying the partition of unity constraint.

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