Anna, Kit Ian Kou, University of Macau, Macau

Outer preserving in Hardy spaces

Abstract

The goal of this talk is to characterize the semigroup of bounded linear operators on the Hardy space H^p(D) that preserve the set of shifted outer functions. The outer functions play a crucial role in the Beurling factorization, where every function in the Hardy space can be expressed as a product of outer and inner functions, the inner functions being the part containing the zeros. A complete description of this semigroup of operators is given. This work is motivated by digital signal processing in the context of geophysical imaging. The class of shifted outer functions represents delayed, causal, minimum-phase signals that model impulsive physical sources.