Generalized coorbit theory, Banach frames, and the relation to \({\alpha}\)-modulation spaces. (English) Zbl 1215.42035

Dahlke, Stephan; Fornasier, Massimo; Rauhut, Holger; Steidl, Gabriele; Teschke, Gerd

Proc. Lond. Math. Soc. (3) 96, No. 2, 464-506 (2008).

Summary: 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 \({\alpha}\)-modulation spaces.

MSC:

42C15	General harmonic expansions, frames
42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems
46E15	Banach spaces of continuous, differentiable or analytic functions
57S25	Groups acting on specific manifolds
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems