20190201
Continuous wavelet transform of schwartz tempered distributions in S'(ℝ n )
Publication
Publication
Symmetry , Volume 11  Issue 2
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 nonconstant distribution which is not equal to the sum of a nonconstant distribution with a nonzero constant distribution.
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doi.org/10.3390/sym11020235  
Symmetry  
Organisation  School of Mathematics and Statistics 
Pandey, J. N, Maurya, J.S. (Jay Singh), Upadhyay, S.K. (Santosh Kumar), & Srivastava, H.M. (Hari Mohan). (2019). Continuous wavelet transform of schwartz tempered distributions in S'(ℝ
n
). Symmetry, 11(2). doi:10.3390/sym11020235
