Pandey, Jagdish NarayanMaurya, Jay SinghUpadhyay, Santosh KumarSrivastava, H. M.2019-03-022019-03-0220192019Pandey, 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/sym11020235http://dx.doi.org/10.3390/sym11020235http://hdl.handle.net/1828/10632In 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.enfunction spaces and their dualsdistributionstempered distributionsSchwartz testing function spacegeneralized functionsdistribution spacewavelet transform of generalized functionsFourier transformArticleDepartment of Mathematics and Statistics