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Sum Rules For Jacobi Matrices And Their Applications To Spectral Theory

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  • Dr. Bashir Eissa Mohammed Abdelrahman

Abstract

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.

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  • Dr. Bashir Eissa Mohammed Abdelrahman, 2021. "Sum Rules For Jacobi Matrices And Their Applications To Spectral Theory," Journal of Statistics and Actuarial Research, IPRJB, vol. 5(1), pages 21-38.
    • Handle: RePEc:bdu:ojjsar:v:5:y:2021:i:1:p:21-38:id:1482
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