LP decomposition of abstract Besov norms in terms of band-limited functions

Abstract Besov spaces were introduced by Butzer and Berens ‘67 in terms of modulus of
continuity. In this talk I will discuss these spaces for any given Hilbert space in terms of the
Littlewood-Paley (LP) decomposition and “smooth band-limited functions”. I will start by
introducing band-limited functions for abstract Hilbert spaces with respect to any self- adjoint
positive definite operator. Then I show how to obtain a discrete version of Calderon reproducing
formula for the Hilbert space, and the Littlewood-Paley decomposition of abstract Besov norms in
terms of band-limited functions.
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