The theory of reproducing systems on locally compact abelian groups

Kutyniok, Gitta und Labate, Demetrio (2006): The theory of reproducing systems on locally compact abelian groups. In: Colloquium Mathematicum, Vol. 106, No. 2: pp. 197-220

Abstract

A reproducing system is a countable collection of functions {φj : j ∈ J } such that a general function f can be decomposed as f = ∑ j∈J cj (f ) φj , with some control on the analyzing coefficients cj (f ). Several such systems have been introduced very successfully in mathematics and its applications. We present a unified viewpoint to 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). As an application of this result, we obtain a new characterization of Parseval frame generators for Gabor and affine systems on L2(G).

• Item Type: Journal article
• Keywords: Affine systems; frames; Gabor systems; locally compact groups; wavelets
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0010-1354
• Language: English