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• # Artykuł - szczegóły

## Colloquium Mathematicum

2006 | 106 | 2 | 197-220

## The theory of reproducing systems on locally compact abelian groups

EN

### Abstrakty

EN
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).

197-220

wydano
2006

### Twórcy

autor
• Institute of Mathematics, Justus-Liebig-University Giessen, Arndtstr. 2, 35392 Giessen, Germany
autor
• Department of Mathematics, North Carolina State University, Campus Box 8205, Raleigh, NC 27695, U.S.A.