Compactness criteria in function spaces

Monika Dörfler, Hans G. Feichtinger, and Karlheinz Gröchenig. "Compactness criteria in function spaces." Colloquium Mathematicae 94.1 (2002): 37-50. <http://eudml.org/doc/284411>.

@article{MonikaDörfler2002,
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 $L²(ℝ^\{d\})$, and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov-Triebel-Lizorkin, modulation and Bargmann-Fock spaces.},
author = {Monika Dörfler, Hans G. Feichtinger, Karlheinz Gröchenig},
journal = {Colloquium Mathematicae},
keywords = {function spaces; wavelet transform; Besov spaces; Triebel-Lizorkin spaces},
language = {eng},
number = {1},
pages = {37-50},
title = {Compactness criteria in function spaces},
url = {http://eudml.org/doc/284411},
volume = {94},
year = {2002},
}

TY - JOUR
AU - Monika Dörfler
AU - Hans G. Feichtinger
AU - Karlheinz Gröchenig
TI - Compactness criteria in function spaces
JO - Colloquium Mathematicae
PY - 2002
VL - 94
IS - 1
SP - 37
EP - 50
AB - 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.
LA - eng
KW - function spaces; wavelet transform; Besov spaces; Triebel-Lizorkin spaces
UR - http://eudml.org/doc/284411
ER -