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Analytic representations with wavelet expansions. (English) Zbl 0837.41017

Summary: The analytic representation of a function or a distribution on the real line is given in terms of series of “analytic wavelets.” These series converge uniformly in compact subsets of the upper and lower half plane. The analytic wavelets used satisfy the same dilation equation as the orthogonal wavelets on the real axis.

MSC:

41A30 Approximation by other special function classes
30B99 Series expansions of functions of one complex variable
46F20 Distributions and ultradistributions as boundary values of analytic functions
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