Representation of all maximally accretive differential operators for first order

Rukiye Öztürk Mert, Pembe İpek Al, Zameddin I. Ismailov

Öz


In the present paper, we construct the minimal and maximal operators generated by special type linear differential-operator expression for first order in the weighted Hilbert space of vector-functions defined on right semi-axis with the use of standard technique. In this case, the minimal operator is accretive but not maximal. Our main goal in this paper is to describe the general form of all maximally accretive extensions of the minimal operator in the weighted Hilbert space of vector-functions.  Using the Calkin-Gorbachuk method, the general representation of all maximally accretive extensions of this minimal operator in terms of boundary conditions is obtained. We also investigate the structure of the spectrum set such maximally accretive extensions of this type of minimal operator. 


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Referanslar


Gorbachuk, V.L. and Gorbachuk, M.L., Boundary value problems for operator differential equations, Kluwer Academic Publisher, Dordrecht, (1991).

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Levchuk, V.V., Smooth maximally dissipative boundary-value problems for a parabolic equation in a Hilbert Space, Ukrainian Mathematic Journal, 35, 4, 502-507, (1983).

Hörmander, L., On the theory of general partial differential operators, Acta Mathematica, 94, 161-248, (1955).

Naimark, M.A., Linear differential operators, Frederick Ungar Publishing Company, New York, USA, (1968).


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