Related papers: Spectral asymptotics for the semiclassical Dirichl…

Under suitable conditions on the asymptotic decay of the metric, we compute the essential spectrum of the Laplace-Beltrami operator acting on $p$-forms on asymptotically hyperbolic manifolds.

We consider a Dirichlet to Neumann operator $\mathcal{L}_a$ arising in a model for water waves, with a nonlocal parameter $a\in(-1,1)$. We deduce the expression of the operator in terms of the Fourier transform, highlighting a local…

A formula is given in terms of secondary characteristic classes for the leading order contribution to the spectral flow for a path of twisted Dirac operators on an odd dimensional, Riemannian manifold when the twisting is done by a path of…

We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive $\delta'$ interaction supported by a smooth surface in $\R^3$, either infinite and asymptotically planar, or compact and closed. Its second term is…

We consider the perturbed Stark operator $H_q\varphi = -\varphi" + x\varphi + q(x)\varphi$, $\varphi(0)=0$, in $L^2(\mathbb{R}_+)$, where $q$ is a real-valued function that belongs to $\mathfrak{A}_r =\left\{…

Let $P$ be a symmetric $2a$-order classical strongly elliptic pseudodifferential operator with even symbol $p(x,\xi )$ on $R^n$ ($0<a<1$), for example a perturbation of $(-\Delta )^a$. Let $\Omega \subset R^n$ be bounded, and let $P_D$ be…

In this paper, we investigate asymptotics of the continuous graph Laplace operator on a smooth Riemannian manifold $(M,g)$ admitting an isolated singularity $x$. We show that if the curvature function $\kappa$ doesn't grow too fast near…

We consider the asymptotic expansion of the functional series \[S_{\mu,\gamma}(a;\lambda)=\sum_{n=1}^\infty \frac{n^\gamma e^{-\lambda n^2/a^2}}{(n^2+a^2)^\mu}\] for real values of the parameters $\gamma$, $\lambda>0$ and $\mu\geq0$ as…

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 revisit a representation for the Riemann zeta function $\zeta(s)$ expressed in terms of normalised incomplete gamma functions given by the author and S. Cang in Methods Appl. Anal. {\bf 4} (1997) 449--470. Use of the uniform asymptotics…

We study the asymptotic distribution of the resonances near the Landau levels $\Lambda\_q =(2q+1)b$, $q \in \mathbb{N}$, of the Dirichlet (resp. Neumann, resp. Robin) realization in the exterior of a compact domain of $\mathbb{R}^3$ of the…

For non-critical almost Mathieu operators with Diophantine frequency, we establish exponential asymptotics on the size of spectral gaps, and show that the spectrum is homogeneous. We also prove the homogeneity of the spectrum for…

We study spectral asymptotics for a large class of differential operators on an open subset of $\R^d$ with finite volume. This class includes the Dirichlet Laplacian, the fractional Laplacian, and also fractional differential operators with…

we obtain the asympotics for the counting function of resonances for a matrix valued schrodinger operator in dimension one.

We continue the study of the A-amplitude associated to a half-line Schrodinger operator, -d^2/dx^2+ q in L^2 ((0,b)), b <= infinity. A is related to the Weyl-Titchmarsh m-function via m(-\kappa^2) =-\kappa - \int_0^a A(\alpha)…

Let $ \Lambda (s) := \Gamma(s+1)\, (1-2^{1-s}) \, \zeta(s) $, and denote its set of zeros by $ Z_\Lambda := Z_\zeta \cup Z_\mathrm{p} $, where $ Z_\zeta $ consists of the nontrivial zeros of $ \zeta(s) $ and $ Z_\mathrm{p} $ those of the…

The study of resonances of the Schr\"{o}dinger operator has a long-standing tradition in mathematical physics. Extensive theoretical investigations have explored the proximity of resonances to the real axis, their distribution, and bounds…

The Dirac operator d+delta on the Hodge complex of a Riemannian manifold is regarded as an annihilation operator A. On a weighted space L_mu^2 Omega, [A,A*] acts as multiplication by a positive constant on excited states if and only if the…

In this paper, by a new method we establish the Weyl-type asymptotic formula for the counting function of biharmonic Stekloff eigenvalues with Neumann boundary condition in a bounded domain of an $n$-dimensional Riemannian manifold.

The well known Weyl's asymptotic formula gives an approximation to the number $\mathcal{N}_{\omega}$ of eigenvalues (counted with multiplicities) on an interval $[0,\>\omega]$ of the Laplace-Beltrami operator on a compact Riemannian…