The structure of test functions that determine weighted composition operators

Abstract

Operators that preserve minimum phase signals, or delayed minimum phase signals, have been shown to be important in practical signal processing contexts, and specifically in geophysical imaging, where one seeks to identify such operators using test signals. Which sets of test signals suffice to recover an unknown operator of the given type? In the present paper we answer this question by relating it to the identification of weighted composition operators acting on analytic functions on the disk. We provide an explicit parameterization of all minimal sets of test functions that identify weighted composition operators on the disk, and then apply the parameterization to construct realistic test signals for use in the geophysical context.