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.
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Schulz-Baldes, H. Geometry of Weyl theory for Jacobi matrices with matrix entries. JAMA 110, 129–165 (2010). https://doi.org/10.1007/s11854-010-0004-5
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DOI: https://doi.org/10.1007/s11854-010-0004-5