Related papers: Continuity properties of multilinear localization …
Local Weyl modules over two-dimensional currents with values in $gl_r$ are deformed into spaces with bases related to parking functions. Using this construction we 1) propose a simple proof that dimension of the space of diagonal…
A multivariate polynomial is {\em stable} if it is nonvanishing whenever all variables have positive imaginary parts. We classify all linear partial differential operators in the Weyl algebra $\A_n$ that preserve stability. An important…
A finite Hilbert space can be associated to a periodic phase space, that is, a torus. A finite subgroup of operators corresponding to reflections and translations on the torus form respectively the basis for the discrete Weyl…
We aim at constructing an analog of the Weyl calculus in an infinite dimensional setting, in which the usual configuration and phase spaces are ultimately replaced by infinite dimensional measure spaces, the so-called abstract Wiener…
Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is…
In this paper we have studied Fourier multipliers and Littlewood-Paley square functions in the context of modulation spaces. We have also proved that any bounded linear operator from modulation space $\mathcal{M}_{p,q}(\R^n), 1\leq p,q\leq…
This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients of certain frame expansions of the kernel of an integral operator are in (\ell^{2,p}), then…
We develop our earlier approach to the Weyl calculus for representations of infinite-dimensional Lie groups by establishing continuity properties of the Moyal product for symbols belonging to various modulation spaces. For instance, we…
We introduce an operator valued Short-Time Fourier Transform for certain classes of operators with operator windows, and show that the transform acts in an analogous way to the Short-Time Fourier Transform for functions, in particular…
In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on $L^p$-spaces. First, we prove…
This paper deals with positivity properties for a pseudodifferential calculus, generalizing Weyl's classical quantization, and set on an infinite dimensional phase space, the Wiener space. In this frame, we show that a positive symbol does…
We consider bilinear multipliers that appeared as a distinguished particular case in the classification of two-dimensional bilinear Hilbert transforms by Demeter and Thiele [9]. In this note we investigate their boundedness on Sobolev…
Given a polynomial P of partial derivatives of the Kahler metric, expressed as a linear combination of directed multigraphs, we prove a simple criterion in terms of the coefficients for $P$ to be an invariant polynomial, i.e. invariant…
It is shown that if V is a local monoidal pseudovariety of semigroups, then K(m)V, D(m)V and LI(m)V are local. Other operators of the form Z(m)(_) are considered. In the process, results about the interplay between operators Z(m)(_) and…
We obtain new multilinear multiplier theorems for symbols of restricted smoothness which lie locally in certain Sobolev spaces. We provide applications concerning the boundedness of the commutators of Calder\'on and…
Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…
Pseudo-differential and Fourier series operators on the n-torus are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
We prove that the Moyal multiplier algebras of the generalized Gelfand-Shilov spaces of type $S$ contain Palamodov spaces of type $\mathcal E$ and the inclusion maps are continuous. We also give a direct proof that the Palamodov spaces are…
We give a geometric interpretation of the Siegel operators for holomorphic differential forms on Siegel modular varieties. This involves extension of the differential forms over a toroidal compactification, and we show that the Siegel…