A generalization of Calderon’s theorem. Discretization of continuous wavelet transforms

Abstract

Calderon’s theorem is generalized to the set of periodic functions belonging to the space L2(0,1). The discretization of the direct and inverse wavelet transforms are realized on the basis of the discrete Fourier transform, which allows one to develop efficient computational algorithms. The Mexican hat wavelet is considered as an example. The work is supported by the Russian Foundation for Basic Research (project no.~08-01-00285).