Related papers: Sturm intersection theory for periodic Jacobi matr…
One of the first theorems in perturbation theory claims that for an arbitrary self-adjoint operator A there exists a perturbation B of Hilbert-Schmidt class, which destroys completely the absolutely continuous spectrum of A (von Neumann).…
We give a simple proof of Borg type uniqueness Theorems for periodic Jacobi operators with matrix valued coefficients.
The Melnikov method is applied to periodically perturbed open systems modeled by an inverse--square--law attraction center plus a quadrupolelike term. A compactification approach that regularizes periodic orbits at infinity is introduced.…
A comparative discussion of the normal form and action angle variable method is presented in a tutorial way. Normal forms are introduced by Lie series which avoid mixed variable canonical transformations. The main interest is focused on…
We establish Lieb-Thirring power bounds on discrete eigenvalues of Jacobi operators for Schatten class complex perturbations of periodic and more generally finite gap Jacobi matrices.
We look for best partitions of the unit interval that minimize certain functionals defined in terms of the eigenvalues of Sturm-Liouville problems. Via \Gamma-convergence theory, we study the asymptotic distribution of the minimizers as the…
An inverse spectral problem is studied for the matrix Sturm-Liouville operator on a finite interval with the general self-adjoint boundary condition. We obtain a constructive solution based on the method of spectral mappings for the…
The problem of the Hamiltonian matrix in the oscillator and Laguerre basis construction from the S-matrix is treated in the context of the algebraic analogue of the Marchenko method.
We prove rate of convergence results for singular perturbations of Hamilton-Jacobi equations in unbounded spaces where the fast operator is linear, uniformly elliptic and has an Ornstein-Uhlenbeck-type drift. The slow operator is a fully…
In this paper, the inverse Sturm-Liouville problem with distribution potential and with polynomials of the spectral parameter in one of the boundary conditions is considered. We for the first time prove local solvability and stability of…
The paper is concerned with the effect of the spatio-temporal heterogeneity on the principal eigenvalue of some linear time-periodic parabolic system. Various asymptotic behaviors of the principal eigenvalue and its monotonicity, as a…
We give a complete description of the set of spectral data (eigenvalues and specially introduced norming constants) for Sturm--Liouville operators on the interval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$ and…
We consider an inverse optimization spectral problem for the Sturm-Liouville operator $$\mathcal{L}[q] u:=-u''+q(x)u$$ subject to the separated boundary conditions. In the main result, we prove that this problem is related to the existence…
We consider an intersection of past and future property of multivariate stationary processes which is the key to deriving various representation theorems for their linear predictor coefficient matrices. We extend useful spectral…
In this article we obtain the asymptotic formulas for the eigenvalues and eigenfunctions of the self-adjoint operator generated by a system of Sturm-Liouville equations with summable coefficients and the quasiperiodic boundary conditions.…
The Cayley-Hamilton theorem is used to implement an iterative process for the efficient numerical computation of matrix power series and their differentials. In addition to straight-forward applications in lattice gauge theory simulations…
We consider the 1D periodic Jacobi matrices. The spectrum of this operator is purely absolutely continuous and consists of intervals separated by gaps. We solve the inverse problem (including characterization) in terms of vertical slits on…
We take advantage of the Sturm-Liouville eigenvalue problem to analytically study the holographic insulator/superconductor phase transition in the probe limit. The interesting point is that this analytical method can not only estimate the…
A method for approximate solution of spectral problems for Sturm-Liouville equations based on the construction of the Delsarte transmutation operators is presented. In fact the problem of numerical approximation of solutions and eigenvalues…
This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid…