INVERSE SPECTRAL PROPARTIES FOR SYMMETRIC OPERATORS WITH WEYL FUNCTIONS

Authors

  • Dr. Bashir Eissa Mohammad Abedrahaman Nyala University College of Science and Education , Sudan

DOI:

https://doi.org/10.47604/jsar.1607

Keywords:

symmetric operator, adjoin extensions, Nevanlinna functions, Weyl functions.

Abstract

We prove that an operator measure in general is non-orthogonal and unbounded and two orthogonal spectral measures are unitarily equivalent. In accordance with the stieltjes inversion formula the spectral measure admits an analytic continuation .We discuss and prove a sharp estimate that a strictly monotone function on each component interval of the inverse function is analytic and also strictly monotone with Weyl functions.

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References

Johames F. Brasche, M. Malamud and Hagen Weyl function and Spectral properties of self-adjoint extensions-Berlin-Germany.

Ju. M. Berezanskii "Expansion in Eigen functions of self-adjoin Operator" Naukova Dumka, Kiev Eng. transl. Amer. Math. R. I., (1968).

J.F. Brache, H. Neidhardt, J. Weidmann, on the point spectrum of Self-adjoint extensions, Math Zeischr,.

J.F. Brache, H.Neidhardt, on the singular continuous spectrum of self -Adjoint extensions. Math. Zeitschr.

J. F. Brache, M. M. Malamud and H., Neidhanlt Weyl functions and Singular continuous spectra of self -adjoint extensions. Gesztesy. Fritz(ed) et al. Stochastic processes and physics and geometry. Germany (1999).

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Published

2022-08-04

How to Cite

Abedrahaman, B. (2022). INVERSE SPECTRAL PROPARTIES FOR SYMMETRIC OPERATORS WITH WEYL FUNCTIONS. Journal of Statistics and Actuarial Research, 6(1), 20–42. https://doi.org/10.47604/jsar.1607

Issue

Vol. 6 No. 1 (2022)

Section

Articles

License

Copyright (c) 2022 Dr. Bashir Eissa Mohammad Abedrahaman

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