We study the space of tempered ultradistributions whose convolutions with test functions are all contained in a given translation-modulation invariant Banach ultradistributions. Our main result will be first structural theorem for aforementioned space. As an application we consider several extensions convolution.

Abstract We demonstrate how to construct spectral triples for twisted group $$C^*$$ C? -algebras of lattices in phase space a second-countable locally compact abelian using class weights appearing time–frequency analysis. This yields way constructing quantum $$C^k$$ xmlns:m...

We discuss the relevance to deformation quantization of Feichtinger’s modulation spaces, especially of the weighted Sjöstrand classesM s (R). These function spaces are good classes of symbols of pseudodifferential operators (observables). They have a widespread use in time-frequency analysis and related topics, but are not very well-known in physics. It turns out that they are particularly well...

By using tools of time-frequency analysis, we obtain some improved local well-posedness results for the NLS, NLW and NLKG equations with Cauchy data in modulation spaces M 0,s .

By using tools of time-frequency analysis, we obtain some improved local well-posedness results for the NLS, NLW and NLKG equations with Cauchy data in modulation spaces M 0,s.

The aim of this paper is to develop a theory of decomposition of the functions belonging to the modulation space M with 0 < p, q ≤ ∞. We shall define molecules for the modulation spaces. The main difficulty in developing our theory lies in the synthesis part, that is, we shall tackle the norm estimate when we are given a sum of molecules under some suitable coefficient conditions. As an applica...

In this paper, we study a class of pseudodifferential operators known as time-frequency localization operators, which depend on symbol $\varsigma$ and two windows functions $g_1$ $g_2$. We first present some basic properties the windowed Opdam-Cherednik transform. Then, use modulation spaces associated with transform appropriate classes for symbols windows, boundedness compactness spaces. Final...

A b s t r a c t. Let Wp,q be the Fourier modulation space FMp,q and let ∗σ be the twisted convolution. If a ∈ D′ such that (a ∗σ φ,φ) ≥ 0 for every φ ∈ C∞ 0 , and χ ∈ S such that χ(0) 6= 0, then we prove that χa ∈ Wp,∞ iff a ∈ Wp,∞. We also present some extensions to the case when weighted Fourier modulation spaces are used. AMS Mathematics Subject Classification (2000): 47B65, 35A21, 35S05

We prove new well-posedness results for energy-critical nonlinear Schrödinger equations in modulation spaces. This covers initial data with infinite mass and energy. The proof is carried out via bilinear refinements adapted function