This article is cited in 3 papers

On linear relations generated by a differential expression and by a Nevanlinna operator function

V. M. Bruk

Saratov State Technical University, 77, Politechnicheskaya Str., Saratov 410054, Russia

Abstract: The families of maximal and minimal relations generated by a differential expression with bounded operator coefficients and by a Nevanlinna operator function are defined. These families are proved to be holomorphic. In the case of finite interval, the space of boundary values is constructed. In terms of boundary conditions, a criterion for the restrictions of maximal relations to be continuously invertible and a criterion for the families of these restrictions to be holomorphic are given. The operators inverse to these restrictions are stated to be integral operators. By using the results obtained, the existence of the characteristic operator on the finite interval and the axis is proved.

Key words and phrases: Hilbert space, linear relation, differential expression, holomorphic family of relations, resolvent, characteristic operator, Nevanlinna function.

MSC: 47A06, 47A10, 34B27

Received: 22.04.2010

Language: English

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