相关论文: Spectral properties of the logarithmic Laplacian

We consider a second order self-adjoint operator in a domain which can be bounded or unbounded. The boundary is partitioned into two parts with Dirichlet boundary condition on one of them, and Neumann condition on the other. We assume that…

For a bounded corner domain $\Omega$, we consider the Robin Laplacian in $\Omega$ with large Robin parameter. Exploiting multiscale analysis and a recursive procedure, we have a precise description of the mechanism giving the ground state…

This paper investigates the recent Connes-Consani-Moscovici $D_{\log}^{(\lambda, N)}$ operators, whose spectra are currently hypothesized to approach the zeros of $\zeta\left(\frac{1}{2} +is\right)$ as $\lambda, N \rightarrow \infty$. It…

We study asymptotic distribution of eigen-values $\omega$ of a quadratic operator polynomial of the following form $(\omega^2-L(\omega))\phi_\omega=0$, where $L(\omega)$ is a second order differential positive elliptic operator with…

We consider the "Method of particular solutions" for numerically computing eigenvalues and eigenfunctions of the Laplacian $\Delta$ on a smooth, bounded domain Omega in RR^n with either Dirichlet or Neumann boundary conditions. This method…

In this paper, we study an inverse spectral operator for the higher-order differential equation $(-1)^my^{(2m)}+ q y = \lambda y$, where $q \in L^2(0,\pi)$. We prove that if $\|q\|_2$ is sufficiently small, the two spectra corresponding to…

We study the spectrum of two kinds of operators involving a conical geometry: the Dirichlet Laplacian in conical layers and Schr\"odinger operators with attractive $\delta$-interactions supported by infinite cones. Under the assumption that…

We study the asymptotic behaviour of the eigenvalues of the Laplace-Beltrami operator on a compact hypersurface in \mathds{R}^{n+1} as it is flattened into a singular double-sided flat hypersurface. We show that the limit spectral problem…

We consider the twisted waveguide $\Omega_\theta$, i.e. the domain obtained by the rotation of the bounded cross section $\omega \subset {\mathbb R}^{2}$ of the straight tube $\Omega : = \omega \times {\mathbb R}$ at angle $\theta$ which…

In this paper we study the Dirichlet eigenvalue problem $$ -\Delta_p u-\Delta_{J,p}u =\lambda|u|^{p-2}u \quad \text{ in } \Omega,\quad u=0 \quad\text{ in } \Omega^c=\mathbb{R}^N\setminus\Omega. $$ Here $\Delta_p u$ is the standard local…

We derive a number of spectral results for Dirac operators in geometrically nontrivial regions in $\mathbb{R}^2$ and $\mathbb{R}^3$ of tube or layer shapes with a zigzag type boundary using the corresponding properties of the Dirichlet…

We make a spectral analysis of discrete Schroedinger operators on the half-line, subject to complex Robin-type boundary couplings and complex-valued potentials. First, optimal spectral enclosures are obtained for summable potentials.…

Let $\Omega$ be an open set in $\R^d$ $(d > 1)$ and $h(\Omega)$ the Fr\'echet space of harmonic functions on $\Omega$. Given a bounded linear operator $L :h(\Omega)\to h(\Omega)$, we show that its eigenvalues $\lambda_n$, arranged in…

This paper focuses on the spectral properties of a bounded self-adjoint operator in $L_2(\mathds R^d)$ being the sum of a convolution operator with an integrable convolution kernel and an operator of multiplication by a continuous potential…

We report the results of a detailed study of the spectral properties of Laplace and Stokes operators, modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, $\eta$,…

We study spectral stability estimates of the Dirichlet eigenvalues of the Laplacian in non-convex domains $\Omega\subset\mathbb R^2$. With the help of these estimates we obtain asymptotically sharp inequalities of ratios of eigenvalues in…

In this paper, we give some lower bounds for several eigenvalues. Firstly, we investigate the eigenvalues $\lambda_i$ of the Laplace operator and prove a sharp lower bound. Moreover, we extent this estimate of the eigenvalues to general…

The purpose of this paper is to explore the asymptotics of the eigenvalue spectrum of the Laplacian on 2 dimensional spaces of constant curvature, giving strong experimental evidence for a conjecture of the second author…

The fractional Laplacian operator, $-(-\triangle)^{\frac{\alpha}{2}}$, appears in a wide class of physical systems, including L\'evy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which…

We study spectral stability estimates of elliptic operators in divergence form $-\textrm{div} [A(w) \nabla g(w)]$ with the Dirichlet boundary condition in non-Lipschitz domains $\widetilde{\Omega} \subset \mathbb C$. The suggested method is…