Continuous Wavelet Transform of Schwartz Tempered Distributions in S′ ( R n )

In this paper, we define a continuous wavelet transform of a Schwartz tempered distribution f ∈ S ′ ( R n ) with wavelet kernel ψ ∈ S ( R n ) and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of S ′ ( R n ) . It turns out that the wavelet transform...

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Bibliographic Details
Published in:Symmetry (Basel) Vol. 11; no. 2; p. 235
Main Authors: Pandey, Jagdish Narayan, Maurya, Jay Singh, Upadhyay, Santosh Kumar, Srivastava, Hari Mohan
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.02.2019
Subjects:
Continuous wavelet transform
Fourier transforms
Mathematical functions
Topology
Wavelet transforms
ISSN:2073-8994, 2073-8994
Online Access:Get full text
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Summary:In this paper, we define a continuous wavelet transform of a Schwartz tempered distribution f ∈ S ′ ( R n ) with wavelet kernel ψ ∈ S ( R n ) and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of S ′ ( R n ) . It turns out that the wavelet transform of a constant distribution is zero and our wavelet inversion formula is not true for constant distribution, but it is true for a non-constant distribution which is not equal to the sum of a non-constant distribution with a non-zero constant distribution.
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym11020235