Compactness Criteria in Function Spaces
Monika Dörfler, Hans G. Feichtinger, Karlheinz Gröchenig
Abstract
The classical criterion for compactness in Banach spaces of functions can be reformulated into a simple tightness condition in the time-frequency domain. This description preserves more explicitly the symmetry between time and frequency than the classical conditions. The result is first stated and proved for L2(Rd), and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov-Triebel-Lizorkin spaces, modulation spaces and Bargmann-Fock spaces.
Create a lesson
Related papers
Independent Backward Preimages and Algebraic Radial Decompositions of Operators
Zakariae Aznay, Fadil Chabbabi, Hassan Zariouh
Spectral and mapping properties of the inverse Ornstein--Uhlenbeck operator
Tommaso Bruno, Valentina Casarino, Paolo Ciatti et al.
Dual Banach spaces with AP but without BAP
Longfa Sun, Zhenguo Wei, Zhendong Xu et al.
Real alternative Daugavet property without Daugavet property in a separable complex Banach space
Jinghao Huang, Ran Xu
Nonisomorphic separable Banach spaces at Lipschitz distance one
Ryotaro Tanaka
Szegő quasiforms: a Schottky-scheme construction for vertex operator superalgebras
A. Zuevsky