Related papers: Spectral asymptotics for infinite order pseudo-dif…
Originally motivated by a stability problem in Fluid Mechanics, we study the spectral and pseudospectral properties of the differential operator $H_\epsilon = -\partial_x^2 + x^2 + i\epsilon^{-1}f(x)$ on $L^2(R)$, where $f$ is a real-valued…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
The spectrum of a selfadjoint second order elliptic differential operator in $L^2(\mathbb{R}^n)$ is described in terms of the limiting behavior of Dirichlet-to-Neumann maps, which arise in a multi-dimensional Glazman decomposition and…
We investigate the Stark operator restricted to a bounded domain $\Omega\subset\mathbb{R}^2$ with Dirichlet boundary conditions. In the semiclassical limit, a three-term asymptotic expansion for its individual eigenvalues has been…
In this article we study the semiclassical spectral measures associated with Schr\"odinger operators on $R^n$. In particular we compute the first few coefficients of the asymptotic expansions of these measures and, as an application, give…
Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…
Self-adjoint operators on infinite-dimensional spaces with continuous spectra are abundant but do not possess a basis of eigenfunctions. Rather, diagonalization is achieved through spectral measures. The SpecSolve package [SIAM Rev., 63(3)…
It is shown that the nonselfadjoint (and non-normal) linear ordinary differential operators of a certain class are spectral operators of scalar type in the sense of Dunford and Bade. Operators of this kind appear in physical problems such…
In this paper, we are concerned with the asymptotic behavior of the Neumann-Poincare operator for Helmholtz system. By analyzing the asymptotic behavior of spherical Bessel function near the origin and/or approach higher order, we prove the…
The self-adjoint matrix Sturm-Liouville operator on a finite interval with a boundary condition in the general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the considered operator. These…
We study the asymptotic distribution of resonances for scattering by compactly supported potentials in hyperbolic space. We first establish an upper bound for the resonance counting function that depends only on the dimension and the…
We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schr\"{o}dinger-type operator with a confining potential and with principle part a periodic elliptic operator in divergence form. We compare the spectrum to the…
We obtain spectral asymptotics for the quantized derivatives of elements from the first-order homogeneous Sobolev space on the quantum Euclidean space, extending an earlier result of McDonald, Sukochev and Xiong (Commun. Math. Phys. 2020).…
The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations. In the present paper the abstract notion is further developed,…
In this paper, we study harmonic analysis on the affine Poincar\'e group $\mathcal{P}_{aff}$, which is a non-unimodular group, and obtain pseudo-differential operators with operator valued symbols. More precisely, we study the boundedness…
We obtain a number of explicit estimates for quasi-norms of pseudo-differential operators in the Schatten-von Neumann classes $S_q$ with $0<q\le 1$. The estimates are applied to derive semi-classical bounds for operators with smooth or…
In this paper, we continue the analysis of the effects of semiclassical sub principal controlled quasimodes, approximate solutions to P(h)u(h,b), depending on the subprincipal symbol b, which can give spectral insta bility (pseudospectrum).…
We describe a new representation of Hankel operators $H$ as pseudo-differential operators $A$ in the space of functions defined on the whole axis. The amplitudes of such operators $A$ have a very special structure: they are products of…
We consider discrete Schroedinger operator J with Wigner-von Neumann potential not belonging to l^2. We find asymptotics of orthonormal polynomials associated to J. We prove the Weyl-Titchmarsh type formula, which relates the spectral…
We explicitly determine the high-energy asymptotics for Weyl-Titchmarsh matrices associated with general matrix-valued Schr\"odinger operators on a half-line.