Inverse problems for periodic generalized Jacobi matrices

Details Inverse problems for periodic generalized Jacobi matrices Inverse problems for periodic generalized Jacobi matrices

2010-11-26

arxiv.org/abs/1011.5830v2

Mathematics

Classical Analysis and ODEs

11 pages (some typos are corrected)

Scientific paper

Some inverse problems for semi-infinite periodic generalized Jacobi matrices
are considered. In particular, a generalization of the Abel criterion is
presented. The approach is based on the fact that the solvability of the
Pell-Abel equation is equivalent to the existence of a certainly normalized
$J$-unitary $2\times 2$-matrix polynomial (the monodromy matrix).

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