Related papers: Pseudo-differential operators in a Gelfand-Shilov …
We give a complete characterization of the continuity of pseudodifferential operators with symbols in modulation spaces $M^{p,q}$, acting on a given Lebesgue space $L^r$. Namely, we find the full range of triples $(p,q,r)$, for which such a…
Let $G$ be a compact Lie group that acts smoothly on a closed manifold $M$. Using a general Simonenko principle, we derive a novel criterion for the Fredholm property of $G$-pseudodifferential operators acting on Sobolev spaces of sections…
For a class of non-selfadjoint $h$--pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin.…
We consider a specific class of manifolds with singularities, namely, stratified manifolds, and describe a class of pseudodifferential operators (PsiDO) related to differential operators with degeneration of first-order with respect to the…
We define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators, of which we give a complete characterization. Lastly, we prove a generalization of the…
In this work we obtain continuity results on H\"older spaces for operators belonging to a Weyl-H\"ormander calculus for metrics such that the class of the associated operators contains, in particular, certain hypoelliptic laplacians. With…
We analyze a general class of difference operators $H_\varepsilon = T_\varepsilon + V_\varepsilon$ on $\ell^2(\varepsilon \mathbb{Z}^d)$, where $V_\varepsilon$ is a one-well potential and $\varepsilon$ is a small parameter. We construct…
We provide Fredholm conditions for compatible differential operators on certain Lie manifolds (that is, on certain possibly non-compact manifolds with nice ends). We discuss in more detail the case of manifolds with cylindrical, hyperbolic,…
We consider multilinear pseudo-differential operators with symbols in the multilinear H\"ormander class $S_{0,0}$. The aim of this paper is to discuss the boundedness of these operators in the settings of Besov spaces.
We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalized) distribution theoretic result on operators with smooth…
We introduce a notion of an algebra of generalized pseudo-differential operators and prove that a spectral triple is regular if and only if it admits an algebra of generalized pseudo-differential operators. We also provide a self-contained…
Bilinear pseudodifferential operators with symbols in the bilinear analog of all the H\"ormander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise…
We give a construction of quasiminimal fields equipped with pseudo-analytic maps, generalising Zilber's pseudo-exponential function. In particular we construct pseudo-exponential maps of simple abelian varieties, including…
This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…
The aim of this paper is to study $L^p$-boundedness property of the pseudo differential operator associated with a symbol, on rank one Riemannian symmetric spaces of noncompact type, where the symbol satisfies H\"ormander-type conditions…
Let $G$ be a unimodular type I second countable locally compact group and $\hat G$ its unitary dual. We introduce and study a global pseudo-differential calculus for operator-valued symbols defined on $G\times\hat G$, and its relations to…
In this paper we construct the spectral expansion for the differential operator generated in all real line by ordinary differential expression of arbitrary order with periodic complex-valued coefficients by introducing new concepts as…
In some previous papers we have defined and studied a 'magnetic' pseudodifferential calculus as a gauge covariant generalization of the Weyl calculus when a magnetic field is present. In this paper we extend the standard Fourier Integral…
This paper concerns certain $\mod p$ differential operators that act on automorphic forms over Shimura varieties of type A or C. We show that, over the ordinary locus, these operators agree with the $\mod p$ reduction of the $p$-adic theta…
In this paper, we consider the semi-classical setting constructed on nilpotent graded Lie groups by means of representation theory. We analyze the effects of the pull-back by diffeomorphisms on pseudodifferential operators. We restrict to…