The theory of reproducing systems on locally compact abelian groups

• Autorzy: Gitta Kutyniok , Demetrio Labate
• Języki publikacji: 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).

Kategorie tematyczne

• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 43A40: Character groups and dual objects
• 43A70: Analysis on specific locally compact and other abelian groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 106
• Numer: 2
• Strony: 197-220

Daty

wydano

2006

Twórcy

autor

Gitta Kutyniok

• Institute of Mathematics, Justus-Liebig-University Giessen, Arndtstr. 2, 35392 Giessen, Germany

autor

Demetrio Labate

• Department of Mathematics, North Carolina State University, Campus Box 8205, Raleigh, NC 27695, U.S.A.

Identyfikatory

DOI

10.4064/cm106-2-3