Jürgen Prestin, Ewald Quak
Optimal Functions for a Periodic Uncertainty Principle and Multiresolution Analysis
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series, {For automorphic theory, See mainly 11F30}

Abstract: In this paper, it is shown that certain Theta functions are
asymptotically optimal for the periodic time frequency uncertainty
principle described by Breitenberger in [2]. These extremal functions
give rise to a periodic multiresolution analysis where corresponding
wavelets also show similar localization properties.
Keywords: Unschärfeprinzip, uncertainty principle periodic wavelets