Related papers: Commutator Criteria for Magnetic Pseudodifferentia…

The theme of this work is that the theory of charged particles in a uniform magnetic field can be generalized to a large class of operators if one uses an extended a class of Weyl operators which we call "Landau--Weyl pseudodifferential…

Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying the general framework to univariate polynomials, one is led to…

The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct…

Motivated by the recent paper of Boggiatto-Garello in J. Pseudo-Differ. Oper. Appl. \textbf{11} (2020), 93-117, where a Gabor operator is regarded as pseudodifferential operator with symbol $p(x,\omega)$ periodic on both the variables, we…

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…

In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of Coifman-Meyer. These new classes allow us to consider operators closely related to the…

For an arbitrary pseudo-differential operator $A:\mathcal{S}(\mathbb{R}% ^{n})\longrightarrow\mathcal{S}^{\prime}(\mathbb{R}^{n})$ with Weyl symbol $a\in\mathcal{S}^{\prime}(\mathbb{R}^{2n})$, we consider the pseudo-differential operators…

By taking the Weyl equation with external electro-magnetic potentials as the simplest representative for a system of PDOs, we give a new method of treating non-commutativity of coefficients matrices. More precisely, we construct a Fourier…

We define and study pseudo-differential operators on a class of fractals that include the post-critically finite self-similar sets and Sierpinski carpets. Using the sub-Gaussian estimates of the heat operator we prove that our operators…

In this paper we construct examples of commutative rings of difference operators with matrix coefficients from representation theory of quantum groups, generalizing the results of our previous paper to the $q$-deformed case. A generalized…

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…

Motivated by the problem of channel estimation in wireless communications, we derive a reconstruction formula for pseudodifferential operators with a bandlimited symbol. This reconstruction formula uses the diagonal entries of the matrix of…

We establish analogues of Liouville's theorem in the complex function theory, with the differential operator replaced by various difference operators. This is done generally by the extraction of (formal) Taylor coefficients using a residue…

We produce, on general homogeneous groups, an analogue of the usual H\"ormander pseudodifferential calculus on Euclidean space, at least as far as products and adjoints are concerned. In contrast to earlier works, we do not limit ourselves…

Using the procedures in \cite{Bu} and \cite{GMS} and the magnetic pseudodifferential calculus we have developped in \cite{MP1,MPR1,IMP1,IMP2} we construct an effective Hamitonian that describes the spectrum in any compact subset of the real…

Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations…

In this note we present a symbolic pseudo-differential calculus on the Heisenberg group. We particularise to this group our general construction [4,3,2] of pseudo-differential calculi on graded groups. The relation between the Weyl…

We prove a sharp Weyl estimate for the number of eigenvalues belonging to a fixed interval of energy of a self-adjoint difference operator acting on $\ell^2(\epsilon\mathbb{Z}^d)$ if the associated symplectic volume of phase space in…

The purpose of this paper is to develop a new theory of gauges in mixed characteristic. Namely, let $k$ be a perfect field of characteristic $p>0$ and $W(k)$ the $p$-typical Witt vectors. Making use of Berthelot's arithmetic differential…

We consider pseudodifferential operators on functions on $\R^{n+1}$ which commute with the Euler operator, and can thus be restricted to spaces of functions homogeneous of some given degree. Their symbols can be regarded as functions on a…