Banach Convolution Algebras of Functions II.
On a New Segal Algebra.
Multipliers of Banach Spaces of Functions on Groups.
Zur Idealtheorie von Segal-Algebren.
Results on Banach ideals and spaces of multipliers.
On a class of convolution algebras of functions
The Banach spaces defined in this paper consist essentially of those elements of ( being a locally compact group) which can in a certain sense be well approximated by functions with compact support. The main result of this paper is the fact that in many cases becomes a Banach convolution algebra. There exist many natural examples. Furthermore some theorems concerning inclusion results and the structure of these spaces are given. In particular we prove that simple conditions imply the existence...
Banach Spaces Related to Integrable Group Representations and Their Atomic Decompositions. Part II.
Individual factorization in Banach modules
Wiener amalgam spaces for the fundamental identity of Gabor analysis.
In the last decade it has become clear that one of the central themes within Gabor analysis (with respect to general time-frequency lattices) is a duality theory for Gabor frames, including the Wexler-Raz biorthogonality condition, the Ron-Shen duality principle and the Janssen representation of a Gabor frame operator. All these results are closely connected with the so-called , which we derive from an application of Poisson's summation formula for the symplectic Fourier transform. The new aspect...
Compactness criteria in function spaces
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 , and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov-Triebel-Lizorkin, modulation and Bargmann-Fock spaces.
On a family of weighted convolution algebras.
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