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, Bd. 106, Nr. 2: S. 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).

• Dokumententyp: Zeitschriftenartikel
• Keywords: Affine systems; frames; Gabor systems; locally compact groups; wavelets
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Professur für Mathematische Grundlagen des Verständnisses der künstlichen Intelligenz
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0010-1354
• Sprache: Englisch