Abstract:In this work the spectral theory of self-adjoint operator A represented by Jacobi matrix is considered. The approach is based on the continued fraction representation of the resolvent matrix element of A. Different criteria of absolute continuity of a spectrum are found. For the analysis of the absolutely continuous spectrum it is used an approximation of A by a sequence of operators A n with absolutely continuous spectrum on a given interval [a, b ] which converges to A in a strong sense on a dense set. In th… Show more
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