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Compactness criteria in function spaces

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Dörfler M., Feichtinger H., Gröchenig K.

Colloquium Mathematicum

2002

tom 94

nr 1

37-50

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 $L²(ℝ^{d})$, and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov-Triebel-Lizorkin, modulation and Bargmann-Fock spaces.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Dörfler M.

1 Feichtinger H.

1 Gröchenig K.

1 2002

Wyniki wyszukiwania

Compactness criteria in function spaces