INVERSE SPECTRAL PROPARTIES FOR SYMMETRIC OPERATORS WITH WEYL FUNCTIONS
DOI:
https://doi.org/10.47604/jsar.1607Keywords:
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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Copyright (c) 2022 Dr. Bashir Eissa Mohammad Abedrahaman
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