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The theory of reproducing systems on locally compact abelian groups

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Kutyniok G., Labate D.

Colloquium Mathematicum

2006

tom 106

nr 2

197-220

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

Ograniczanie wyników

1 Colloquium Mathematicum

1 Kutyniok G.

1 Labate D.

1 2006

Wyniki wyszukiwania

The theory of reproducing systems on locally compact abelian groups