Killip–Simon problem and Jacobi flow on GMP matrices

Seminar on Jacobi Matrices

Two modified Jacobi methods for M-matrices

Jacobi matrices

We discuss the relationships among Jacobi matrices, orthogonal polynomials, spectral measure, moments, minors, Gaussian quadrature, resolvents and continued fractions in the simplest setting, namely the finite-dimensional one. The formal structure is essentially the same as that in the infinite-dimensional setting, where it leads into the rich analytic world of orthogonal polynomials on the rea...

Periodic GMP Matrices

We recall criteria on the spectrum of Jacobi matrices such that the corresponding isospectral torus consists of periodic operators. Motivated by those known results for Jacobi matrices, we define a new class of operators called GMP matrices. They form a certain Generalization of matrices related to the strong Moment Problem. This class allows us to give a parametrization of almost periodic fini...

On a Spectral Property of Jacobi Matrices

Let J be a Jacobi matrix with elements bk on the main diagonal and elements ak on the auxiliary ones. We suppose that J is a compact perturbation of the free Jacobi matrix. In this case the essential spectrum of J coincides with [−2, 2], and its discrete spectrum is a union of two sequences {xj }, x + j > 2, x − j < −2, tending to ±2. We denote sequences {ak+1 − ak} and {ak+1 + ak−1 − 2ak} by ∂...