Related papers: Eigenvalue asymptotics for randomly perturbed non-…

We find the Weyl law followed by the eigenvalues of contractive maps. An important property is that it is mainly insensitive to the dimension of the corresponding invariant classical set, the strange attractor. The usual explanation for the…

The spectral problem for the high order differential operator with singular weight is considered. If the weight is a generalized derivative of self-similar function with zero spectral degree the asymptotics of eigenvalues is obtained. They…

We investigate the behaviour of the eigenvalues of two-dimensional Pauli operators with nonconstant magnetic fields perturbed by a sign-indefinite decaying electric potential V. We prove new eigenvalues asymptotics.

We study the pseudospectrum of a class of non-selfadjoint differential operators. Our work consists in a detailed study of the microlocal properties, which rule the spectral stability or instability phenomena appearing under small…

In previous papers, a generalization of the Weyl calculus was introduced in connection with the quantization of a particle moving in $\mathbb R^n$ under the influence of a variable magnetic field $B$. It incorporates phase factors defined…

We study spectral asymptotics for small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part possesses several invariant Lagrangian tori…

We provide a direct proof of Weyl's law for the buckling eigenvalues of the biharmonic operator on a wide class of domains of $\mathbb R^d$ including bounded Lipschitz domains. The proof relies on asymptotically sharp lower and upper bounds…

We prove an asymptotic estimate for the growth of variational eigenvalues of fractional p-Laplacian eigenvalue problems on a smooth bounded domain.

In this paper, we will prove the Weyl's law for the asymptotic formula of Dirichlet eigenvalues on metric measure spaces with generalized Ricci curvature bounded from below.

We discuss asymptotic behavior of the eigenvalue distribution of the differential form Laplacian on a Riemannian foliated manifold when the metric on the ambient manifold is blown up in directions normal to the leaves (in the adiabatic…

We study small, PT-symmetric perturbations of self-adjoint double-well Schr\"odinger operators in dimension $n\geq 1$. We prove that the eigenvalues stay real for a very small perturbation, then bifurcate to the complex plane as the…

Small perturbations of the Jacobi matrix with weights \sqrt n and zero diagonal are considered. A formula relating the asymptotics of polynomials of the first kind to the spectral density is obtained, which is analogue of the classical…

We prove Weyl type of asymptotic formulas for the real and the complex internal transmission eigenvalues when the domain is a ball and the index of refraction is constant.

We prove quantitative bounds on the eigenvalues of non-selfadjoint bounded and unbounded operators. We use the perturbation determinant to reduce the problem to one of studying the zeroes of a holomorphic function.

We investigate Weyl type asymptotics of functional-difference operators associated to mirror curves of special del Pezzo Calabi-Yau threefolds. These operators are $H(\zeta)=U+U^{-1}+V+\zeta V^{-1}$ and $H_{m,n}=U+V+q^{-mn}U^{-m}V^{-n}$,…

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for…

Let $G\subset \O(n)$ be a group of isometries acting on $n$-dimensional Euclidean space $\R^n$, and ${\bf{X}}$ a bounded domain in $\R^n$ which is transformed into itself under the action of G. Consider a symmetric, classical…

Let $N(T;V)$ denote the number of eigenvalues of the Schr\"odinger operator $-y'' + Vy$ with absolute value less than $T$. This paper studies the Weyl asymptotics of perturbations of the Schr\"odinger operator $-y'' + \frac{1}{4}e^{2t}y$ on…

We study the spectra of general $N\times N$ Toeplitz matrices given by symbols in the Wiener Algebra perturbed by small complex Gaussian random matrices, in the regime $N\gg 1$. We prove an asymptotic formula for the number of eigenvalues…

For a two-dimensional Schr\"odinger operator $H_{\alpha V}=-\Delta-\alpha V,\ V\ge 0,$ we study the behavior of the number $N_-(H_{\alpha V})$ of its negative eigenvalues (bound states), as the coupling parameter $\alpha$ tends to infinity.…