Continuous wavelet transform of Schwartz tempered distributions

The continuous wavelet transform of Schwartz tempered distributions is investigated and derive the corresponding wavelet inversion formula (valid modulo a constant-tempered distribution) interpreting convergence in . But uniqueness theorem for the present wavelet inversion formula is valid for the s...

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Bibliographic Details
Published in:Cogent mathematics & statistics Vol. 6; no. 1; p. 1623647
Main Authors: Pandey, J.N., Upadhyay, S.K.
Format: Journal Article
Language:English
Published: Abingdon Cogent 01.01.2019
Taylor & Francis Ltd
Subjects:
Applied mathematics
Continuous wavelet transform
distribution spaces
distributions
Fourier transforms
function spaces and their duals
generalized functions
Primary: 46F12
Secondary: 46F05
Uniqueness theorems
Wavelet analysis
wavelet transform of generalized functions
Wavelet transforms
ISSN:2574-2558, 2574-2558, 2768-4830
Online Access:Get full text
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Summary:The continuous wavelet transform of Schwartz tempered distributions is investigated and derive the corresponding wavelet inversion formula (valid modulo a constant-tempered distribution) interpreting convergence in . But uniqueness theorem for the present wavelet inversion formula is valid for the space obtained by filtering (deleting) (i) all non-zero constant distributions from the space , (ii) all non-zero constants that appear with a distribution as a union. As an example, in considering the distribution we would omit 1 and retain only . The wavelet kernel under consideration for determining the wavelet transform are those wavelets whose all the moments are non-zero. As an example, is such a wavelet. is an arbitrary constant. There exist many other classes of such wavelets. In our analysis, we do not use a wavelet kernel having any of its moments zero.
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ISSN:2574-2558
2574-2558
2768-4830
DOI:10.1080/25742558.2019.1623647