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The theory of reproducing systems on locally compact abelian groups

Gitta KutyniokDemetrio Labate — 2006

Colloquium Mathematicae

A reproducing system is a countable collection of functions ϕ j : j such that a general function f can be decomposed as f = j c j ( f ) ϕ j , with some control on the analyzing coefficients c j ( f ) . Several such systems have been introduced very successfully in mathematics and its applications. We present a unified viewpoint in the study of reproducing systems on locally compact abelian groups G. This approach gives a novel characterization of the Parseval frame generators for a very general class of reproducing systems on L²(G)....

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