This paper is concerned with the construction of atomic decompositions and Banach frames for subspaces of certain Banach spaces consisting of elements which are invariant under some symmetry group. These Banach spaces – called coorbit spaces – are related to an integrable group representation. The construction is established via a generalization of the well-established Feichtinger-Gröchenig the...

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 L (R), and then generalized to coorbit spaces. As special cases, we obtain new characte...

In this paper, we establish the asymptotic estimates for norms of matrix dilation operators on modulation spaces. As an application, study boundedness spaces Hausdorff operators. The definition are also revisited fitting our study.

The objective of this paper is to report on recent progress on Strichartz estimates for the Schrödinger equation and to present the state-of-the-art. These estimates have been obtained in Lebesgue spaces, Sobolev spaces and, recently, in Wiener amalgam and modulation spaces. We present and compare the different technicalities. Then, we illustrate applications to well-posedness.

We deduce trace properties for modulation spaces (including certain Wiener-amalgam spaces) of Gelfand–Shilov distributions.We use these results to show that [Formula: see text]dos with amplitudes in suitable spaces, agree normal type whose symbols belong (other) spaces. In particular we extend earlier include quasi-Banach also apply our on Schatten-von Neumann and nuclear

We generalize the classical coorbit space theory developed by Feichtinger and Gröchenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best n-term approximation schemes. We apply the abstract theory to time-frequency analysis of modul...