The theory of reproducing systems on locally compact abelian groups

Gitta Kutyniok; Demetrio Labate

Colloquium Mathematicae, Tome 106 (2006), p. 197-220 / Harvested from The Polish Digital Mathematics Library

Résumé

A reproducing system is a countable collection of functions $ϕ_{j} : j \in$ such that a general function f can be decomposed as $f = \sum_{j \in} c_{j} (f) ϕ_{j}$ , 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). As an application, we obtain a new characterization of Parseval frame generators for Gabor and affine systems on L²(G).

Publié le : 2006-01-01

Zbl 1113.43008

EUDML-ID : urn:eudml:doc:286281

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Gitta Kutyniok; Demetrio Labate. The theory of reproducing systems on locally compact abelian groups. Colloquium Mathematicae, Tome 106 (2006) pp. 197-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-3/