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

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dc.contributor.authorPandey, Jagdish Narayan
dc.contributor.authorMaurya, Jay Singh
dc.contributor.authorUpadhyay, Santosh Kumar
dc.contributor.authorSrivastava, H. M.
dc.date.accessioned2019-03-02T16:45:03Z
dc.date.available2019-03-02T16:45:03Z
dc.date.copyright2019en_US
dc.date.issued2019
dc.description.abstractIn 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.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.identifier.citationPandey, J.N., Maurya, J.S., Upadhyay, S.K. & Srivastava, H.M. (2019). Continuous Wavelet Transform of Schwartz Tempered Distributions in S′ ( R n ). Symmetry, 11(2), 235. https://doi.org/10.3390/sym11020235en_US
dc.identifier.urihttp://dx.doi.org/10.3390/sym11020235
dc.identifier.urihttp://hdl.handle.net/1828/10632
dc.language.isoenen_US
dc.publisherSymmetryen_US
dc.subjectfunction spaces and their duals
dc.subjectdistributions
dc.subjecttempered distributions
dc.subjectSchwartz testing function space
dc.subjectgeneralized functions
dc.subjectdistribution space
dc.subjectwavelet transform of generalized functions
dc.subjectFourier transform
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleContinuous Wavelet Transform of Schwartz Tempered Distributions in S′ ( R n )en_US
dc.typeArticleen_US

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