Abstract
The concept of the multiplicity of the continuum spectrum is introduced for a class of dissipative quasihermitian operators. A formula is given for calculating it in terms of the nonnegative component of the polar expansion of the difference of the limiting values of the characteristic matrix-function.
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REFERENCES
A. V. Kuzhel, Characteristic Function and Models of Nonself-adjoint Operators, Kluwer, Dordrecht (1996).
N. I. Akhiezer andI. M. Glazman, Theory of Linear Operators in Hilbert Space [in Russian], Vishcha Shkola, Kharkov (1977), Vol. 1.
L. A. Sakhnovich, “Dissipative operators with absolutely continuous spectra, ” in: Trudy Mosk. Mat. Ob-va, 19, 211–270 (1968).
Yu. P. Moskaleva, “Unbounded dissipative operators, ” in: Trudy Matematicheskogo Fakulteta, (1997), pp. 88–89.
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Moskaleva, Y.P. Multiplicity Characteristic of the Continuum Spectrum of a Class of Dissipative Operators. Journal of Mathematical Sciences 107, 4464–4466 (2001). https://doi.org/10.1023/A:1012577122098
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DOI: https://doi.org/10.1023/A:1012577122098