ﻻ يوجد ملخص باللغة العربية
This note considers Sturm oscillation theory for regular matrix Sturm-Liouville operators on finite intervals and for matrix Jacobi operators. The number of space oscillations of the eigenvalues of the matrix Prufer phases at a given energy, defined by a suitable lift in the Jacobi case, is shown to be equal to the number of eigenvalues below that energy. This results from a positivity property of the Prufer phases, namely they cannot cross $-1$ in the negative direction, and is also shown to be closely linked to the positivity of the matrix Prufer phase in the energy variable. The theory is illustrated by numerical calculations for an explicit example.
We consider Sturm-Liouville problems on the finite interval. We show that spectral data for the case of Dirichlet boundary conditions are equivalent to spectral data for Neumann boundary conditions. In particular, the solution of the inverse problem
We propose two ways for determining the Greens matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from the Jacobi-
We study perturbations of the self-adjoint periodic Sturm--Liouville operator [ A_0 = frac{1}{r_0}left(-frac{mathrm d}{mathrm dx} p_0 frac{mathrm d}{mathrm dx} + q_0right) ] and conclude under $L^1$-assumptions on the differences of the coefficient
Let $dot A$ be a densely defined, closed, symmetric operator in the complex, separable Hilbert space $mathcal{H}$ with equal deficiency indices and denote by $mathcal{N}_i = ker big(big(dot Abig)^* - i I_{mathcal{H}}big)$, $dim , (mathcal{N}_i)=kin m
Explicit formulas for the analytic extensions of the scattering matrix and the time delay of a quasi-one-dimensional discrete Schrodinger operator with a potential of finite support are derived. This includes a careful analysis of the band edge singu