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Generalized coorbit theory, Banach frames, and the relation to α‐modulation spaces
Author(s) -
Dahlke Stephan,
Fornasier Massimo,
Rauhut Holger,
Steidl Gabriele,
Teschke Gerd
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm051
Subject(s) - mathematics , modulation space , modulo , affine transformation , pure mathematics , banach space , interpolation space , smoothness , heisenberg group , topos theory , lp space , space (punctuation) , quotient , general theory , algebra over a field , discrete mathematics , mathematical analysis , functional analysis , mathematical economics , biochemistry , chemistry , gene , art , linguistics , philosophy , literature
This paper is concerned with generalizations and specific applications of the coorbit space theory based on group representations modulo quotients, which has been developed quite recently. We show that the general theory applied to the affine Weyl–Heisenberg group gives rise to families of smoothness spaces that can be identified with α‐modulation spaces.