Geometry of Weyl theory for Jacobi matrices with matrix entries
TLDR
In this article, the Weyl surface describing the dependence of Green's matrix on the boundary conditions is interpreted as the set of maximally isotropic subspaces of a quadratic form given by the Wronskian.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 subspaces of a quadratic form 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 calculated explicitly.read more
Citations
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References
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Book
Spectral Theory of Ordinary Differential Operators
TL;DR: In this paper, the separation of the Dirac operator was discussed and the Lagrange identity for n>2 was proved for the case of Dirac systems with self-adjoint differential expressions.
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The Classical Moment Problem as a Self-Adjoint Finite Difference Operator
TL;DR: In this paper, a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators is presented, where the Nevanlinna functions appear as elements of a transfer matrix and convergence of Pade approximants appears as the strong resolvent convergence of finite matrix approximations to a Jacobi matrix.
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