Approximation of Weyl-Heisenberg frame operators
type: Item
instance of: scholarly article
title: Approximation of Weyl-Heisenberg frame operators
zbMATH Open document ID: 1356.42021
author: T. C. Easwaran Nambudiri
author: K. Parthasarathy
published in: Complex Analysis and Operator Theory
publication date: 2017-01-17T00:00:00Z
review text: Approximations of the inverse of Weyl-Heisenberg frame (Gabor frame) operators have been studied by \textit{P. G. Casazza} and \textit{O. Christensen} [J. Approx. Theory 103, No. 2, 338--356 (2000; Zbl 0951.46008)] by using finite dimensional truncations. It has been observed that study on approximations of these operators by positive operators for the same kind with nice generators has not done so extensively and the nice generators like compactly supported smooth functions may not always yield frames, however, they generate Bessel sequences (preframes). Thus, approximations using preframe operators rather than frame operators have been investigated in this paper. Also, it has been shown that such approximations are possible in the weak operator topology under mild conditions on the window function \(g\geq 0\) and in the strong operator topology in some special cases. Moreover, the approximations of Weyl-Heisenberg frame operators by Weyl-Heisenberg preframe operators generated by compactly supported smooth functions have been presented.
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 47B65
zbMATH DE Number: 6675403
zbMATH Keywords: Bessel sequence
zbMATH Keywords: Weyl-Heisenberg frame
zbMATH Keywords: Gabor frame
zbMATH Keywords: frame operator
zbMATH Keywords: Gabor Bessel sequence operator
reviewed by: Devendra Kumar
MaRDI profile type: Publication
full work available at URL: s11785-016-0532-9
OpenAlex ID: W2294157216
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DOI: 10.1007/S11785-016-0532-9
description: scientific article; zbMATH DE number 6675403