Wavelet Operators on Distributions and Stochastic Processes
We investigate the properties of wavelet operators on the space L2(R) and on the space of tempered distributions. Then we show that all accessible wavelets in an augmented set still form a collection of irreducible unitary representations of locally compact groups in L2(R) and in the space of tempered distributions. Thus, we extend the theory to L2-integrable stochastic processes. We discuss the isometry, characterization of the range, inversion associated with these accessible wavelets. Then we find the continuous extensions of Banach spaces associated with these wavelet operators and reproducing operators.