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
Copyright Status
Unknown
Socpus ID
84867992880 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84867992880
STARS Citation
Gu, Qing and Han, Deguang, "Functional Gabor Frame Multipliers" (2003). Scopus Export 2000s. 1352.
https://stars.library.ucf.edu/scopus2000/1352