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

Date

2019

Authors

Pandey, Jagdish Narayan
Maurya, Jay Singh
Upadhyay, Santosh Kumar
Srivastava, H. M.

Journal Title

Journal ISSN

Volume Title

Publisher

Symmetry

Abstract

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.

Description

Keywords

function spaces and their duals, distributions, tempered distributions, Schwartz testing function space, generalized functions, distribution space, wavelet transform of generalized functions, Fourier transform

Citation

Pandey, 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/sym11020235