Related papers: Spectral Asymptotics for Operators of Hormander Ty…
The Bloch--Torrey operator $-h^2\Delta+e^{i\alpha}x_1$ on a bounded smooth planar domain, subject to Dirichlet boundary conditions, is analyzed. Assuming $\alpha\in\left[0,\frac{3\pi}{5}\right)$ and a non-degeneracy assumption on the…
We consider the Schr\"odinger operators $H_V=-\Delta_g+V$ with singular potentials $V$ on general $n$-dimensional Riemannian manifolds and study whether various forms of pointwise Weyl law remain valid under this pertubation. We prove that…
Let $A$ be an elliptic pseudo-differential operator of order $m$ on a closed manifold $\mathcal{X}$ of dimension $n>0$, formally positive self-adjoint with respect to some positive smooth density $d\mu_\mathcal{X}$. Then, the spectrum of…
This is the second in a series of two articles where we study various aspects of the spectral theory associated to families of hyperbolic Riemann surfaces obtained through elliptic degeneration. In the first article, we investigate the…
A self-adjoint operator is constructed on the $L_2$-functions on the $K$-rational points $X(K)$ of a Mumford curve $X$ defined over a non-archimedean local field $K$. It generates a Feller semi-group, and the corresponding heat equation…
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 the operator ${\mathcal A}_h=-\Delta+iV$ in the semi-classical $h\rightarrow 0$, where $V$ is a smooth real potential with no critical points. We obtain both the left margin of the spectrum, as well as resolvent estimates on the…
In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…
We consider a semiclassical asymptotics of local trace for the 3D-Schroedinger operator with self-generated magnetic field; it is given by Weyl expression with O(h^{-1}) error and under standard condition to Hamiltonian trajectories even…
We consider the heat equation in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to an improvement of the decay rate of the heat…
We study spectral properties of Hamiltonians $\rH_{X,\gB,q}$ with $\delta'$-point interactions on a discrete set $X={x_k}_{k=1}^\infty\subset\R_+$. %at the centers $x_n$ on the positive half line in terms of energy forms. Using the form…
In this article, we provide the spectral analysis of a Dirac-type operator on $\mathbb{Z}^2$ by describing the behavior of the spectral shift function associated with a sign-definite trace-class perturbation by a multiplication operator. We…
We study the eigenvalues of Schr\"odinger type operators $T + \lambda V$ and their asymptotic behavior in the small coupling limit $\lambda \to 0$, in the case where the symbol of the kinetic energy, $T(p)$, strongly degenerates on a…
The aim of this paper is to establish the solvability and global regularity theory for a new class of generalized anisotropic heat-type boundary value problems with (pure) dynamical anisotropic Wentzell boundary conditions. We first prove…
We consider the Schroedinger operator H on L^2(R^2) or L^2(R^3) with constant magnetic field and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of…
We survey some known results about operator semigroup generated by operator matrices with diagonal or coupled domain. These abstract results are applied to the characterization of well-/ill-posedness for a class of evolution equations with…
We consider a magnetic Schr\"odinger operator $H^h$, depending on a semiclassical parameter $h>0$, on a compact Riemannian manifold. We assume that there is no electric field. We suppose that the minimal value $b_0$ of the intensity of the…
In this paper we prove that the heat kernel $k$ associated to the operator $A:= (1+|x|^\alpha)\Delta +b|x|^{\alpha-1}\frac{x}{|x|}\cdot\nabla -|x|^\beta$ satisfies $$ k(t,x,y) \leq c_1e^{\lambda_0 t+…
We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the…
We consider self-adjoint realizations of a second-order elliptic differential expression on ${\mathbb R}^n$ with singular interactions of $\delta$ and $\delta^\prime$-type supported on a compact closed smooth hypersurface in ${\mathbb…