Title

Functional Gabor Frame Multipliers

Keywords

functional Gabor frame multiplier; Gabor frame; wavelet frame

Abstract

A Gabor frame multiplier is a bounded operator that maps normalized tight Gabor frame generators to normalized tight Gabor frame generators. While characterization of such operators is still unknown, we give a complete characterization for the functional Gabor frame multipliers. We prove that a L ∞ -function h is a functional Gabor frame multiplier (for the time-frequency lattice aℤ × bℤ) if and only if it is unimodular and h(t)/h(t + 1/b) is a-periodic. Along the same line, we also characterize all the Gabor frame generators g (resp. frame wavelets ψ) for which there is a function ω ∈ L ∞(ℝ) such that {wg mn} (resp. ωψ k,ℓ) is a normalized tight frame. © 2003 Mathematica Josephina, Inc.

Publication Date

12-1-2003

Publication Title

Journal of Geometric Analysis

Volume

13

Issue

3

Number of Pages

467-478

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/BF02922054

Socpus ID

84867992880 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84867992880

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