Accretive Canonical Type Quasi-Differential Operators for First Order

Accretive Canonical Type Quasi-Differential Operators for First Order

In this work, using the method Calkin-Gorbachuk all maximal accretive extensions of the minimaloperator generated by linear canonical type quasi-differential operator expression in the weighted Hilbert spaceof the vector functions defined at right semi-axis are described. Lastly, geometry of spectrum set of these typeextensions will be investigated.

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  • [1] Arlinskii, Yu. M., On proper accretive extensions of positive linear relations , Ukrainian Mat. Zh. 47(6) (1995), 723-730.
  • [2] Arlinskii, Yu. M., Abstract boundary conditions for maximal sectorial extensions of sectorial operators , Math. Nachr. 209 (2000), 5-36.
  • [3] Arlinskii, Yu. M., Operator Methods for Boundary Value Problems, London Math. Soc. Lecture Note Ser., 404, Cambridge Univ. Press, Londan, 2012.
  • [4] Arlinskii, Yu. M., Kovalev, Yu., Tsekanovskii, E., Accretive and sectorial extensions of nonnegative symmetric operators , Complex Anal. Oper. Theory 6 (2012), 677-718.
  • [5] Arlinskii, Yu. M., Popov, A. B., m-Accretive extensions of a sectorial operator , Sbornik: Mathematics 204 (2013), 1085-1121.
  • [6] Evans, W. D., On the extension problem for accretive differential operators, Journal of Functional Analysis 63 (1985), 276-298.
  • [7] Fischbacher, C., The nonproper dissipative extensions of a dual pair , Trans. Amer. Math. Soc. 370 (2018), 8895-8920.
  • [8] Gorbachuk, V. I., Gorbachuk, M. L., Boundary Value Problems for Operator Differential Equations, Kluwer Academic Publisher, Dordrecht, 1991.
  • [9] Hormander, L., ¨ On the theory of general partial differential operators, Acta Mathematica 94(1955), 161-248. 2, 3
  • [10] Kato, T., Perturbation Theory for Linear Operators, Springer-Verlag Inc., New York, 1966.
  • [11] Levchuk, V. V., Smooth maximally dissipative boundary-value problems for a parabolic equation in a Hilbert space, Ukrainian Mathematic Journal 35(4) (1983), 502-507.
  • [12] von Neumann, J., Allgemeine eigenwerttheorie hermitescher funktionaloperatoren, Math. Ann. 102 (1929-1931), 49-13