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Abstract: The paper develops theory of covariant transform, which is inspired by thewavelet construction. It was observed that many interesting types of waveletsor coherent states arise from group representations which are not squareintegrable or vacuum vectors which are not admissible. Covariant transformextends an applicability of the popular wavelets construction to classicexamples like the Hardy space H 2, Banach spaces, covariant functional calculusand many others.Keywords: Wavelets, coherent states, group representations, Hardy space,Littlewood-Paley operator, functional calculus, Berezin calculus, Radontransform, Moebius map, maximal function, affine group, special linear group,numerical range, characteristic function, functional model.

Author: Vladimir V. Kisil


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