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Coorbit spaces with voice in a Fréchet space. (English) Zbl 1375.43001

Coorbit space theory was originally introduced by H. Feichtinger and K. Gröchenig in a series of papers in 1988–1989. The authors of the article under review elaborate a new coorbit space theory for reproducing representations of a locally compact second countable group \(G\) that are not necessarily irreducible nor integrable. Their theory is successful in the sense that it provides a substitute for the classical integrability condition, it contains the classical coorbit space theory even for non irreducible representations.

MSC:

43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
42B35 Function spaces arising in harmonic analysis
22D10 Unitary representations of locally compact groups
46A04 Locally convex Fréchet spaces and (DF)-spaces
46F05 Topological linear spaces of test functions, distributions and ultradistributions
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