School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada.
*E-mail: jpandey@math.carleton.ca
AMS Subject Classification [2000]: Primary: 35B65; Secondary: 41A46, 46E45
We define a testing function space DL2 (F) consisting of a class of ∁∞ functions defined on IR and equip it with the topology generated by a separating collection of seminorms on DL2 (F), where k = 0, 1, 2,…. It is proved that for ,
The convergence is being interpreted in the weak generalized sense. Here ψ is the mother wavelet of the Shannon systems, defined by where , and is a complete orthonormal sequence of wavelets in L2(IR). We also define functions {φm,n(t)}m,n∈ℤ by and show that in the weak generalized sense. It is also proved that where c is a nonnegative constant depending upon f.
Many other related results are proved.
wavelet transform, generalized functions, wavelet expansion of generalized functions, orthonormal wavelets
