Geometry of Weyl theory for Jacobi matrices with matrix entries
Mathematical Physics
2016-10-28 v1 math.MP
Abstract
A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal matrix with invertible blocks on the off-diagonals. The Weyl surface describing the dependence of Green's matrix on the boundary conditions is interpreted as the set of maximally isotropic subspace of a quadratic from given by the Wronskian. Analysis of the possibly degenerate limit quadratic form leads to the limit point/limit surface theory of maximal symmetric extensions for semi-infinite Jacobi matrices with matrix entries with arbitrary deficiency indices. The resolvent of the extensions is explicitly calculated.
Keywords
Cite
@article{arxiv.0804.3746,
title = {Geometry of Weyl theory for Jacobi matrices with matrix entries},
author = {Hermann Schulz-Baldes},
journal= {arXiv preprint arXiv:0804.3746},
year = {2016}
}