\(k\)-Hankel Gabor transform on \(\mathbb{R}^d\) and its applications to the reproducing kernel theory
type: Item
instance of: scholarly article
title: \(k\)-Hankel Gabor transform on \(\mathbb{R}^d\) and its applications to the reproducing kernel theory
zbMATH Open document ID: 1486.44007
author: Hatem Mejjaoli
published in: Complex Analysis and Operator Theory
publication date: 2021-05-28T00:00:00Z
review text: In this 54-page-paper, the author considers the so-called \(k\)-Hankel Gabor transform on \({\mathbb R}^d\) with radial windows. He presents the fundamental properties of the Moore-Penrose inverses and reproducing kernels in the \(k\)-Hankel Gabor transform setting, which naturally generate certain applications of the general theory of reproducing kernels to Tikhonov regularization, and also the best approximation of the \(k\)-Hankel Gabor transform on associated generalized Sobolev spaces. Uncertainty principles involving time-frequency representations are also considered as applications of the \(k\)-Hankel Gabor transform. Moreover, time-frequency localization operators are studied, and the spectrogram associated with the \(k\)-Hankel Gabor transform is analysed.
reviewed by: L. P. Castro
Mathematics Subject Classification ID: 44A20
Mathematics Subject Classification ID: 46E22
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 47G30
zbMATH DE Number: 7352432
zbMATH Keywords: \(k\)-Hankel Gabor transform
zbMATH Keywords: generalized Sobolev spaces
zbMATH Keywords: extremal functions
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: time-frequency concentration
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: reproducing kernel
MaRDI profile type: Publication
full work available at URL: s11785-020-01042-x
OpenAlex ID: W3120352462
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\(k\)-Hankel Gabor transform on \(\mathbb{R}^d\) and its applications to the reproducing kernel theory (DOI)
DOI: 10.1007/S11785-020-01042-X