(1) A unified characterization of reproducing systems for square integrable functions on n-dimensional Euclidean space; (2) Various applications of this characterization.

speaker: Guido Weiss (Washington University in St. Louis)

abstract: The Gabor systems are obtained by the action of a countable family of modulations and translations on an appropriate square integrable fuction, similarly, wavelet systems are obtained in an analogous fashion by using translations and dilations. There are many different systems that involve the action of a countable family made up of appropriate collections of translations, modulations and dilations. We state and prove a general theorem that characterizes all these various systems. In the second lecture we show how this general result can be applied in order to obtain a wide variety of such systems that are orthonormal bases or, more generally, Parseval frames.

<< Go back