Related papers: Commutator Criteria for Magnetic Pseudodifferentia…
The aim of this article is to prove a Beals type characterization theorem for pseudodifferential operators in Wiener spaces. The definition of pseudodifferential operators in Wiener spaces and a Calder\'on-Vaillancourt type result appear in…
We review recent results on the magnetic pseudo-differential calculus both in symbolic and in $C^*$-algebraic form. We also indicate some applications to spectral analysis of pseudo-differential operators with variable magnetic fields.
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
We survey some aspects of the pseudo-differential Weyl calculus for irreducible unitary representations of nilpotent Lie groups, ranging from the classical ideas to recently obtained results. The classical Weyl-H\"ormander calculus is…
In this work, we use semigroup integral to evaluate zeta-function regularized determinants. This is especially powerful for non--positive operators such as the Dirac operator. In order to understand fully the quantum effective action one…
The first purpose of this article is to provide conditions for a bounded operator in $L^2(\R^n)$ to be the Weyl (resp. anti-Wick) quantization of a bounded continuous symbol on $\R^{2n}$. Then, explicit formulas for the Weyl (resp.…
We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces both in the quasi-analytic and in the…
In this paper, we study harmonic analysis on the affine Poincar\'e group $\mathcal{P}_{aff}$, which is a non-unimodular group, and obtain pseudo-differential operators with operator valued symbols. More precisely, we study the boundedness…
In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups. The result is applied to give criteria for the ellipticity and the global hypoellipticity of…
We establish a H\"{o}rmander type theorem for the multilinear pseudo-differential operators, which is also a generalization of the results in \cite{MR4322619} to symbols depending on the spatial variable. Most known results for multilinear…
We consider one-point commuting difference operators of rank one. The coefficients of these operators depend on a functional parameter, shift operators being included only with positive degrees. We study these operators in the case of…
Background: Phenomenological Poincar\'e invariant quantum mechanical models can provide an efficient description of the dynamics of strongly interacting particles that is consistent with spectral and scattering observables. These models are…
Starting out from a new description of a class of parameter-dependent pseudodifferential operators with finite regularity number due to G. Grubb, we introduce a calculus of parameter-dependent, poly-homogeneous symbols whose homogeneous…
A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential…
We prove global subelliptic estimates for systems of quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols. In a previous work, we pointed out…
We revisit the celebrated Peierls-Onsager substitution employing the magnetic pseudo-differential calculus for weak magnetic fields with no spatial decay conditions, when the non-magnetic symbols have a certain spatial periodicity. We show…
This article presents a survey of recent developments on pseudodifferential operators on noncommutative tori. We describe currently available constructions of those operators: by means of a $C^*$--dynamical system, by using an analogue of…
In the framework of (vector valued) quantized holomorphic functions defined on non-commutative spaces, ``quantized hermitian symmetric spaces'', we analyze what the algebras of quantized differential operators with variable coefficients…
We consider here pseudo-differential operators whose symbol $\sigma(x,\xi)$ is not infinitely smooth with respect to $x$. Decomposing such symbols into four -sometimes five- components and using tools of paradifferential calculus, we derive…
The Weyl modules are the standard modules for the Schur algebra. Their duals (the costandard modules) have well-known constructions as quotients of exterior powers and as submodules of symmetric powers. This paper presents analogous…