Related papers: Localization Operators On Discrete Modulation Spac…
We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schr\"odinger operators, acting on $L^2(\R)\otimes \C^N$, for arbitrary $N\geq 1$. We prove that, under suitable assumptions on the…
In this paper, we consider the embedding relations between any two $\alpha$% -modulation spaces. Based on an observation that the $\alpha$-modulation space with smaller $\alpha$ can be regarded as a corresponding $\alpha$% -modulation space…
The main result is that every pseudo-differential operator of type 1,1 and order $d$ is continuous from the Triebel--Lizorkin space $F^d_{p,1}$ to $L_p$, $1\le p<\infty$, and that this is optimal within the Besov and Triebel--Lizorkin…
We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in weighted Lebesgue spaces.…
We extend the Bargmann transform to the magnetic pseudodifferential calculus, using gauge-covariant families of coherent states. We also introduce modulation mappings, a first step towards adapting modulation spaces to the magnetic case.
We define localized modulation maps and modulation spaces of symbols suited to the study of Rieffel's deformation quantization pseudodifferential calculus. They are used to generate Hilbert space representations for the quantized…
Wiener-Hopf plus Hankel operators acting between Lebesgue spaces on the real line are studied in view of their invertibility, one sided-invertibility, Fredholm, and semi-Fredholm properties. This is done in two different cases: (i) when the…
Following the operator algebraic approach to Gabor analysis, we construct frames of translates for the Hilbert space localisation of the Morita equivalence bimodule arising from a groupoid equivalence between Hausdorff groupoids, where one…
We deduce continuity properties for pseudo-differential operators with symbols in quasi-Banach Orlicz modulation spaces when rely on other quasi-Banach Orlicz modulation spaces. In particular we extend certain results in…
Time-frequency analysis have played a crucial role in the development of localization operators in the last twenty years. We present its applications to the study of boundedness and Schatten Class property for such operators. In particular,…
We deduce trace properties for modulation spaces of Gelfand-Shilov distributions. We use these properties to show that pseudo-differential operators with amplitudes in suitable modulation spaces, agree with pseudo-differential operators of…
We study a class of Fourier integral operators on compact manifolds with boundary, associated with a natural class of symplectomorphisms, namely, those which preserve the boundary. A calculus of Boutet de Monvel's type can be defined for…
We present in this paper the construction of a pseudodifferential calculus on smooth non-compact manifolds associated to a globally defined and coordinate independant complete symbol calculus, that generalizes the standard…
This paper explores the properties of multipliers associated with discrete analogues of fractional integrals, revealing intriguing connections with Dirichlet characters, Euler's identity, and Dedekind zeta functions of quadratic imaginary…
This work deals with Schr\"odinger equations with quadratic and sub-quadratic Hamiltonians perturbed by a potential. In particular we shall focus on bounded, but not necessarily smooth perturbations. We shall give a representation of such…
We give sufficient conditions on the Lebesgue exponents for compositions of odd numbers of pseudo-differential operators with symbols in modulation spaces. As a byproduct, we obtain sufficient conditions for twisted convolutions of odd…
In this work we study some general classes of pseudodifferential operators whose symbols are defined in terms of phase space estimates.
In this paper, we investigate the mapping properties of pseudo-differential operators with operator-valued symbols. Thanks to the smooth atomic decomposition of the operator-valued Triebel-Lizorkin spaces…
It is a well-known result of Eymard that the Fourier-Stieltjes algebra of a locally compact group $G$ can be identified with the dual of the group $\cs$ $C^{*}(G)$. A corresponding result for a locally compact groupoid $G$ has been…
In this paper, the weighted estimates for multilinear pseudo-differential operators were systematically studied in rearrangement invariant Banach and quasi-Banach spaces. These spaces contain the Lebesgue space, the classical Lorentz space…