Related papers: The magnetic formalism; new results
In previous articles, a magnetic pseudodifferential calculus and a family of C*-algebras associated with twisted dynamical systems were introduced and the connections between them have been established. We extend this formalism to symbol…
In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…
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 introduce a fractional magnetic pseudorelativistic operator for a general fractional order $s\in(0,1)$. First we define a suitable functional setting and we prove some fundamental properties. Then we show the behavior of the operator as…
In this paper we introduce the magnetic Hodge Laplacian, which is a generalization of the magnetic Laplacian on functions to differential forms. We consider various spectral results, which are known for the magnetic Laplacian on functions…
First, we reconsider the magnetic pseudodifferential calculus and show that for a large class of non-decaying symbols, their corresponding magnetic pseudodifferential operators can be represented, up to a global gauge transform, 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…
We prove a symbolic calculus for a class of pseudodifferential operators, and discuss its applications to $L^2$-compactness via a compact version of the $T(1)$ theorem.
In previous papers, a generalization of the Weyl calculus was introduced in connection with the quantization of a particle moving in $\mathbb R^n$ under the influence of a variable magnetic field $B$. It incorporates phase factors defined…
We give a procedure for reconstructing a magnetic field and electric potential from boundary measurements related to the magnetic Schroedinger operator in three and higher dimensions.
The gauge covariant magnetic Weyl calculus has been introduced and studied in previous works. We prove criteria in terms of commutators for operators to be magnetic pseudo-differential operators of suitable symbol classes. The approach is…
In a previous paper ([1]), we associated a holonomy groupoid and a C*-algebra to any singular foliation (M,F). Using these, we construct the associated pseudodifferential calculus. This calculus gives meaning to a Laplace operator of any…
A new symbol theory for pseudodifferential operators in the complex analytic category is given. This theory provides a cohomological foundation of symbolic calculus.
For families of magnetic pseudodifferential operators defined by symbols and magnetic fields depending continuously on a real parameter $\epsilon$, we show that the corresponding family of spectra also varies continuously with $\epsilon$.
This work develops a magnetic pseudodifferential calculus for super operators OpA(F); these map operators onto operators (as opposed to Lp functions onto Lq functions). Here, F could be a tempered distribution or a H\"ormander symbol. An…
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 this paper we study some properties of the field of rational pseudo-differential operators on a field and some other related rings. As an application we reconstruct the Kac co-cycle on the Lie algebra of differential operators on a…
An operator formalism is developed for a description of charged electron-hole complexes in magnetic fields. A novel unitary transformation of the Hamiltonian that allows one to partially separate the center-of-mass and internal motions is…
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…
We extend the matrix representation of magnetic pseudo-differential operators in a tight Gabor frame from [arXiv:1804.05220, arXiv:2212.12229] to asymmetrical quantizations and smooth symbols dominated by a tempered weight (and not just…