Related papers: Resonances for Euler-Bernoulli operator on the hal…
We consider the third order operator with periodic coefficients on the real line. This operator is used in the integration of the non-linear evolution Boussinesq equation. For the minimal smoothness of the coefficients we prove that: 1) the…
We study the spectrum of a periodic self-adjoint operator on the axis perturbed by a small localized nonself-adjoint operator. It is shown that the continuous spectrum is independent of the perturbation, the residual spectrum is empty, and…
This paper studies the resonances of Schr\"odinger operators with bounded, compactly supported, real-valued potentials on d-dimensional Euclidean space, where d is even. If the potential V is non-trivial and d is not 4 then the meromorphic…
In this short paper, the commutator of monomials of operators obeying constant commutation relations is expressed in terms of anticommutators. The formula involves Bernoulli numbers or Euler polynomials evaluated in zero. The role of…
We find an asymptotic expression for the first eigenvalue of the biharmonic operator on a long thin rectangle. This is done by finding lower and upper bounds which become increasingly accurate with increasing length. The lower bound is…
We study Rellich inequalities associated to higher-order elliptic operators in the Euclidean space. The inequalities are expressed in terms of an associated Finsler metric. In the case of half-spaces we obtain the sharp constant while for a…
This paper is concerned with non-Hermitian degeneracy and exceptional points associated with resonances in an acoustic scattering problem with sound-hard obstacles. The aim is to find non-Hermitian degenerate (defective) resonances using…
We study the resonances of (generally, non-selfadjoint) Schr\"odinger operators with matrix-valued square-well potentials. We compute explicitly the Jost function and derive complex transcendental equations for the resonances. We prove…
In this paper, we investigate the eigenvalue problem for a non-local dispersal operator defined on a bounded spatial domain with Neumann-type boundary conditions. Unlike the classical Laplacian, the non-local operator lacks compactness,…
In this work we consider semi-classical Schr\"odinger operators with potentials supported in a bounded strictly convex subset ${\cal O}$ of ${\bf R}^n$ with smooth boundary. Letting $h$ denote the semi-classical parameter, we consider…
In \cite{Os} a general spectral approximation theory was developed for compact operators on a Banach space which does not require that the operators be self-adjoint and also provides a first order correction term. Here we extend some of the…
We consider the Hamiltonian $H$ of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator $H$ has infinitely many eigenvalues of infinite multiplicity embedded in…
We prove a sharp upper bound and a lower bound for the first nonzero eigenvalue of the Wentzell-Laplace operator on compact manifolds with boundary and an isoperimetric inequality for the same eigenvalue in the case where the manifold is a…
In this paper we introduce conformally covariant boundary operators for Poincar\'e-Einstein manifolds satisfying a mild spectral assumption. Using these boundary operators we set up higher order Dirichlet problems whose solutions are such…
In this paper we study the maximum principle, the existence of eigenvalue and the existence of solution for the Dirichlet problem for operators which are fully-nonlinear, elliptic but presenting some singularity or degeneracy which are…
In this paper we extend some existence's results concerning the generalized eigenvalues for fully nonlinear operators singular or degenerate. We consider the radial case and we prove the existence of an infinite number of eigenvalues,…
We extend some recent results of Lubinsky, Levin, Simon, and Totik from measures with compact support to spectral measures of Schr\"odinger operators on the half-line. In particular, we define a reproducing kernel $S_L$ for Schr\"odinger…
We initiate the study of weighted multi-Toeplitz operators associated with noncommutative regular domains in B(H)^n. These operators are acting on the full Fock space with n generators and have as symbols free pluriharmonic functions.…
Superoscillations are a phenomenon in physics, where linear combinations of low-frequency plane waves interfere almost destructively in such a way that the resulting wave has a higher frequency than any of the individual waves. The…
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…