Inverse problems for periodic generalized Jacobi matrices

2010/11/26 by Derevyagin, Maxim
#41A50 #47B36 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 30B70 #Secondary 15A22 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1011.5830

Abstract

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× 2-matrix polynomial (the monodromy matrix).

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