Weighted Coorbit Spaces and
Banach Frames on
Homogeneous Spaces |
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Authors: | Stephan Dahlke Gabriele Steidl Gerd Teschke |
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Institution: | (1) Universität Marburg, Fachbereich Mathematik und Informatik, Hans-Meerwein-Str., Lahnberge, 35032 Marburg, Germany;(2) Universität Mannheim, Fakultät für Mathematik und Informatik, D7, 27, 68131 Mannheim, Germany;(3) Fachbereich 3, Universität Bremen, Postfach 33 04 40, 28334 Bremen, Germany |
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Abstract: | This article is concerned with frame constructions on domains and manifolds. The
starting point is a unitary group representation which is square integrable modulo a suitable
subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized
coorbit spaces can be defined by collecting all functions for which this wavelet transform
is contained in a weighted Lp-space. Moreover, we show that a judicious discretization of the
representation leads to an atomic decomposition and to Banach frames for these coorbit spaces. |
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Keywords: | |
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