Related papers: Weyl asymptotics for pseudodifferential operators …

The Weyl symbolic calculus of operators leads to the construction, if one takes for symbol a certain distribution decomposing over the zeros of the Riemann zeta function, of an operator with the following property: the Riemann hypothesis is…

This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter \eps, the case of small coupling $\lambda$ to the magnetic vector potential naturally occurs in this context.…

We characterize geometrically the regularizing effects of the semigroups generated by accretive non-selfadjoint quadratic differential operators. As a byproduct, we establish the subelliptic estimates enjoyed by these operators, being…

We study the counting function of the eigenvalues for tensor products of operators, and their perturbations, in the context of Shubin classes and closed manifolds. We emphasize connections with problems of analytic number theory, concerning…

We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along…

We outline an abstract approach to the pseudo-differential Weyl calculus for operators in function spaces in infinitely many variables. Our earlier approach to the Weyl calculus for Lie group representations is extended to the case of…

In this letter, by an approach that employs Weyl symbols for operators, a semiclassical theory is developed for the offdiagonal function in the eigenstate thermalization hypothesis, which is for offdiagonal elements…

We deduce eigenvalue asymptotics of the Neumann--Poincar\'e operators in three dimensions. The region $\Omega$ is $C^{2, \alpha}$ ($\alpha>0$) bounded in ${\mathbf R}^3$ and the Neumann--Poincar\'e operator ${\mathcal K}_{\partial\Omega} :…

In this paper we study a family of operators dependent on a small parameter $\epsilon > 0$, which arise in a problem in fluid mechanics. We show that the spectra of these operators converge to N as $\epsilon \to 0$, even though, for fixed…

We study self-adjoint extensions of a second order differential operator of Sturm-Liouville type on a graph. We relate self-adjointness of the operator to the existence of non-complete trajectories of the Hamiltonian vector field defined by…

The classical Weyl-von Neumann theorem states that for any self-adjoint operator $A$ in a separable Hilbert space $\mathfrak H$ there exists a (non-unique) Hilbert-Schmidt operator $C = C^*$ such that the perturbed operator $A+C$ has purely…

We consider a class of pseudodifferential operators with a doubly characteristic point, where the quadratic part of the symbol fails to be elliptic but obeys an averaging assumption. Under suitable additional assumptions, semiclassical…

We consider a non-selfadjoint Dirac-type differential expression \begin{equation} D(Q)y:= J_n \frac{dy}{dx} + Q(x)y, \quad\quad\quad (1) \end{equation} with a non-selfadjoint potential matrix $Q \in L^1_{loc}({\mathcal…

This paper is concerned with the Weyl composition of symbols in large dimension. We specify a class of symbols in order to estimate the Weyl symbol of the product of two Weyl $h-$pseudodifferential operators, with constants independent of…

We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non-trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the…

The spectral properties of non-self-adjoint extensions $A_{[B]}$ of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions. These extensions are given in…

We consider a Schr\"odinger operator with bounded, measurable potential in multidimensional Euclidean space. We prove for every $L^2$-eigenfunction a quantitative equidistribution estimate. It compares the total $L^2$-norm with the…

We consider the eigenvalues of the three-dimensional Weyl operator defined in terms of the (Euclidean) Ashtekar variables, and we study their dependence on the gravitational field. We notice that these eigenvalues can be used as…

Small perturbations of the Jacobi matrix with weights \sqrt n and zero diagonal are considered. A formula relating the asymptotics of polynomials of the first kind to the spectral density is obtained, which is analogue of the classical…

This is the first in a series of works devoted to small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2. In the present work we treat the case when the classical flow of the unperturbed part is…