SUM RULES FOR JACOBI MATRICES AND THEIR APPLICATIONS TO SPECTRAL THEORY - Abdelrahman , Bashir (Journal of Statistics and Actuarial Research, 2021)
The study discusses the proof of and symmetric application of Cases sum rules for Jacobi matrices. Of special interest is a linear combination of these sum rules which have strictly positive terms. The complete classification of the spectral measure of all Jacobi matrices J for which J-J0 is Hilbert space -Achmidt. The study shows the bound of a Jacobi matrix. The description for the point and absolutely continuous spectrum, while for the singular continuous spectrum additional assumptions are needed. The study shows and prove a bound of a Jacobi matrix. And we give complete description for the point and absolutely continuous spectrum, while for the singular continuous spectrum additional assumptions are needed, we prove a characterization of a characteristic function of a row contraction operator and verify its defect operator. We also prove a commutability of an operator of this row contraction.