Analytic representation of generalized tempered distributions of exponential growth by wavelets. (Q1411735)

The authors define the generalized tempered distribution space \({\mathcal K}^r_M\) and multiresolution analysis of \(L^2(\mathbb{R})\) associated with \(\phi\in{\mathcal K}^r_M(\mathbb{R})\) is discussed. Analytic representation of distributions of \({\mathcal K}^{rt}_M\) by wavelets is the subject matter of further study by the authors in the paper. They present an analytic representation of \({\mathcal K}^{rt}_M\) in terms of series of analytic wavelets.