Wavelets Beyond Admissibility

Abstract

The purpose of this paper is to articulate an observation that many interesting type of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors which are not admissible. This extends an applicability of the popular wavelets construction to classic examples like the Hardy space. Keywords: Wavelets, coherent states, group representations, Hardy space, functional calculus, Berezin calculus, Radon transform, Moebius map, maximal function, affine group, special linear group, numerical range.