Quasi-self-adjoint maximal accretive extensions of nonnegative symmetric operators

• Autorzy: Arlinskii Y. , Kovalev Y. , Tsekanovskii E.

Warianty tytułu

RU

Kvazisamosoprjazhennyje maksimal'nyje akkreditivnyje rasshirjenija neorticatelnykhsimmetricheskikh operatorov

• Języki publikacji: EN

Abstrakty

EN

RU

Słowa kluczowe

EN

quasi-self-adjoint; accretive extension; sectorial extension; nonnegative symmetric operator; fractional-linear transformation; parametrization

• Wydawca: -
• Czasopismo: Teka Komisji Motoryzacji i Energetyki Rolnictwa
• Rocznik: 2010
• Tom: 10A
• Opis fizyczny: p.6-14,ref.

Twórcy

autor

Arlinskii Y.

• Department of Mathematical Analysis, East Ukrainian National University, Lugansk, Ukraine

autor

Kovalev Y.

autor

Tsekanovskii E.

Bibliografia

• 1. Albeverio S., Gesztesy F., Hoegh-Krohn R., Holden H, 1988: Solvable models in quantum mechanics. Springer-Verlag, Berlin.
• 2. Ando T., Nishio K., 1970: Positive self-adjoint extensions of positive symmetric operators. Tohoku Math. J. - 22. - P. 65-75.
• 3. Arlinskii Yu. M., 1988: Positive spaces of boundary values and sectorial extensions of nonnegative symmetric operators, Ukrain. Math. Zh, 40, no.1, 8-14 (Russian).
• 4. Arlinskii Yu., 1995: On proper accretive extensions of positive linear relations. Ukrain. Mat. Zh. 47, no. 6, 723-730.
• 5. Arlinskii Yu., Tsekanovskii E., 1982: Nonselfadjoint contracting extensions of a Hermitian contraction and the theorems of M. G. Kreĭn. Uspekhi Mat. Nauk 37, no. 1, 131-132 (Russian).
• 6. Arlinskii Yu., Tsekanovskii E., 2005: The von Neumann problem for nonnegative symmetric operators. Int. Eq. and Oper. Theory, 51, 319-356.
• 7. Arlinskii Yu., Tsekanovskii E., 2009: Krein's research on semi-bounded operators, its contemporary developments, and applications. Operator Theory: Advances and Applications, 190, 65-112.
• 8. Birman M.Sh., 1956: On the theory of self-adjoint extensions of positive definite operators. Mat. Sbornik 38, 431-450 (Russian).
• 9. Crandall M., 1969: Norm preserving extensions of linear transformations on Hilbert spaces. Proc. Amer. Math. Soc. 21, 335-340.
• 10. Derkach V.A., Malamud M.M, Tsekanovskii E.R., 1989: Sectorial extensions of a positive operator, and the characteristic function. Ukrain.Math Zh. 41, no. 2, 151-158 (Russian)
• 11. Derkach V.A., Malamud M.M., 1995: The extension theory of Hermitian operators and the moment problem. J. Math. Sci. 73, no. 2, 141-242.
• 12. Evans, W.D, Knowles, I., 1985: On the extensions problem for accretive differential operators, J. Funct. Anal. 63, no. 3, 276-298.
• 13. Grubb G., 1968: A characterization of the non-local boundary value problems associated with an elliptic operator. Ann. Scuola Norm. Sup. Pisa (3), 22, 425-513.
• 14. Kato T., 1966: Perturbation theory for linear operators. Springer-Verlag.
• 15. Krein M.G., 1947: The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications. I, Mat. Sbornik 20, no. 3, 431-495, II, Mat. Sbornik 21, no.3, 365-404 (Russian).
• 16. Kochubei A.N., 1979: Extensions of a positive definite symmetric operator. Dokl. Akad. Nauk Ukrain. SSR, Ser. A, no. 3, 168-171 (Russian)
• 17. Mikhailets V.A., 1974: Solvable and sectorial boundary value problems for the operator Sturm-Liouville equation. Ukrinian Math Zh., 26, 450-459 (Russian).
• 18. Mil’yo O.Ya., Storoh O.G., 1991: On the general form of a maximally accretive extension of a positive-definite operator.Dokl Akad. Nauk Ukraine, no. 6, 19-22 (Russian).
• 19. Phillips R, 1959: Dissipative operators and hyperbolic systems of partial differential equations, Trans. Amer. Math. Soc., 90, 192-254.