相关论文: Asymptotic formulae and inequalities for point spe…

The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…

We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so…

For a class of non-selfadjoint $h$--pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin.…

We prove sharp criteria on the behavior of radial curvature for the existence of asymptotically flat or hyperbolic Riemannian manifolds with prescribed sets of eigenvalues embedded in the spectrum of the Laplacian. In particular, we…

This paper is to investigate the dependence of the principal spectrum points of nonlocal dispersal operators on underlying parameters and to consider its applications. In particular, we study the effects of the spatial inhomogeneity, the…

We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…

Dealing with one-dimensional diffusion operators, we obtain upper and lower variational formulae on the eigenvalues given by the max-min principle, generalizing the celebrated result of Chen and Wang on the spectral gap. Our inequalities…

In this paper, we give several asymptotic formulas for the number of multiplicatively dependent vectors of algebraic numbers of fixed degree, or within a fixed number field, and bounded height.

We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries perturb in some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner…

In this article we prove upper bounds for the Laplace eigenvalues $\lambda_k$ below the essential spectrum for strictly negatively curved Cartan-Hadamard manifolds. Our bound is given in terms of $k^2$ and specific geometric data of the…

Algebraic Multigrid (AMG) methods have been proven to be effective solvers for large-scale linear algebraic systems $Ax = b$ with Hermitian positive definite (HPD) matrix $A$. For such problems the convergence in the $A$-norm is well…

We provide a necessary and sufficient condition for matrices in the max-plus algebra to be pseudo-diagonalizable, calculate the powers of pseudo-diagonal matrices and prove the invariance of optimal-node matrices and separable matrices…

Under the mild trace-norm assumptions we show that the eigenvalues of a generic (non Hermitian) complex perturbation of a Jacobi matrix sequence (not necessarily real) are still distributed as the real-valued function $2\cos t$ on…

In the broad range of studies related to quantum graphs, quantum graph spectra appear as a topic of special interest. They are important in the context of diffusion type problems posed on metric graphs. Theoretical findings suggest that…

We study averages of multiplicative eigenvalue statistics in ensembles of orthogonal Haar distributed matrices, which can alternatively be written as Toeplitz+Hankel determinants. We obtain new asymptotics for symbols with Fisher-Hartwig…

We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimension $D$ tends to infinity. Our approach is…

Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…

We develop a max-plus spectral theory for infinite matrices. We introduce recurrence and tightness conditions, under which many results of the finite dimensional theory, concerning the representation of eigenvectors and the asymptotic…

The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The extended method uses the knowledge of the…

We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on…