Pandey, J.N.; Maurya, J.S.; Upadhyay, S.K.; Srivastava, H.M. Continuous Wavelet Transform of Schwartz Tempered Distributions in S′ (Rn). Symmetry2019, 11, 235.
Pandey, J.N.; Maurya, J.S.; Upadhyay, S.K.; Srivastava, H.M. Continuous Wavelet Transform of Schwartz Tempered Distributions in S′ (
R
n
). Symmetry 2019, 11, 235.
Pandey, J.N.; Maurya, J.S.; Upadhyay, S.K.; Srivastava, H.M. Continuous Wavelet Transform of Schwartz Tempered Distributions in S′ (Rn). Symmetry2019, 11, 235.
Pandey, J.N.; Maurya, J.S.; Upadhyay, S.K.; Srivastava, H.M. Continuous Wavelet Transform of Schwartz Tempered Distributions in S′ (
R
n
). Symmetry 2019, 11, 235.
Abstract
In this paper we define a continuous wavelet transform of a Schwartz tempered distribution $f \in S^{'}(\mathbb R^n)$ with wavelet kernel $\psi \in S(\mathbb R^n)$ and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of $S^{'}(\mathbb R^n)$. 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.
Keywords
function spaces and their duals; distributions; generalized functions; distribution space; wavelet transform of generalized functions
Subject
Computer Science and Mathematics, Analysis
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
