Coorbit Spaces and Dual Molecules: the Quasi-Banach Case

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Date
2022-05-27MFO Scientific Program
OWRF 2021Series
Oberwolfach Preprints;2022-08Author
Van Velthoven, Jordy Timo
Voigtlaender, Felix
Metadata
Show full item recordOWP-2022-08
Abstract
This paper provides a self-contained exposition of coorbit spaces associated with integrable group representations and quasi-Banach function spaces. It extends the theory in [Studia Math., 180(3):237–253, 2007] to locally compact groups that do not necessarily possess a compact, conjugation-invariant unit neighborhood. Furthermore, the present paper establishes the existence of dual molecules of frames and Riesz sequences as in [J. Funct. Anal., 280(10):56, 2021] for the setting of quasi-Banach spaces. To ensure the direct applicability to various well-studied examples, the theory is developed for possibly projective and reducible unitary representations.