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- Title
Continuous Wavelet Transform of Schwartz Tempered Distributions in S′ (Rn).
- Authors
Pandey, Jagdish Narayan; Maurya, Jay Singh; Upadhyay, Santosh Kumar; Srivastava, Hari Mohan
- 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.
- Subjects
WAVELET transforms; SCHWARTZ distributions; STOCHASTIC convergence; MATHEMATICAL formulas; KERNEL (Mathematics)
- Publication
Symmetry (20738994), 2019, Vol 11, Issue 2, p235
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym11020235