A distribution space for Hilbert transform and its applications
type: Item
instance of: scholarly article
title: A distribution space for Hilbert transform and its applications
zbMATH Open document ID: 1209.46020
published in: Science in China. Series A
publication date: 2009-12-07T00:00:00Z
review text: The author introduces a new space \({\mathcal D}_H\) of test functions for the Hilbert transform as the direct sum of \(\mathcal D\) and \(H({\mathcal D})\), and he shows that the Hilbert transform is naturally extended to the dual space \({\mathcal D}_H'\) by conjugation. Here, \({\mathcal D}\) is the space of infinitely differentiable functions with compact support. Also, some characterizations of the space \({\mathcal D}_H\) are given and some nonlinear phase signals are shown to belong to the space \({\mathcal D}'_H\).
reviewed by: Dohan Kim
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 5643373
zbMATH Keywords: Hilbert transform
zbMATH Keywords: distribution, time-frequency analysis
zbMATH Keywords: circular Hilbert transform
author: Lihua Yang
MaRDI profile type: Publication
full work available at URL: s11425-008-0007-1
OpenAlex ID: W1974024385
cites work: Q4488070
cites work: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
cites work: A B-spline approach for empirical mode decompositions
cites work: The Bedrosian identity for the Hilbert transform of product functions
cites work: Characterization of boundary values of functions in Hardy spaces with applications in signal analysis
cites work: Necessary and sufficient conditions for the Bedrosian identity
cites work: Q4230520
cites work: Q5640160
cites work: Q5579904
cites work: Some Remarks on Analytic Representations and Products of Distributions
cites work: The Hilbert Transform of Schwartz Distributions
cites work: The Hilbert transform of Schwartz distributions. II
cites work: Q4340161
cites work: Q3342799
cites work: Q3735790
cites work: Q3995454
cites work: Q4112938
DOI: 10.1007/S11425-008-0007-1
description: scientific article; zbMATH DE number 5643373