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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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
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Abstract 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.
AbstractList 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.
In this paper, we define a continuous wavelet transform of a Schwartz tempered distribution f∈S′(Rn) with wavelet kernel ψ∈S(Rn) and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of S′(Rn). 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.
Author Pandey, Jagdish Narayan
Maurya, Jay Singh
Srivastava, Hari Mohan
Upadhyay, Santosh Kumar
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  surname: Srivastava
  fullname: Srivastava, Hari Mohan
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Cites_doi 10.1515/anly-2014-1267
10.1016/j.amc.2016.02.013
10.1007/978-3-642-61859-8
10.1142/S0219691316500375
10.1002/9781118032510
10.1017/CBO9780511623820
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10.1007/s10474-012-0263-y
10.1134/S1061920817040124
10.2991/978-94-91216-24-4
10.1090/proc/12590
ContentType Journal Article
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Copyright_xml – notice: 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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In this paper, we define a continuous wavelet transform of a Schwartz tempered distribution f∈S′(Rn) with wavelet kernel ψ∈S(Rn) and derive the corresponding...
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SubjectTerms Continuous wavelet transform
Fourier transforms
Mathematical functions
Topology
Wavelet transforms
Title Continuous Wavelet Transform of Schwartz Tempered Distributions in S′ ( R n )
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