This article is cited in 5 papers

Invertible linear relations generated by an integral equation with a Nevanlinna measure

V. M. Bruk

Chair of Mathematics and Modeling, Saratov State Technical University, Saratov, Russia

Abstract: We define families of maximal and minimal relations generated by integral equations with a Nevanlinna operator measure and a non-selfadjoint operator measure. We prove that if a restriction of a maximal relation is continuously invertible, then the operator inverse to this restriction is integral. We establish a sufficient condition ensuring that the convergence of non-selfadjoint operator measures implies the convergence of the corresponding integral operators inverse to restrictions of maximal relations. The obtained results are applicable to differential equations with singular coefficients.

Keywords: Hilbert space, linear relation, integral equation, holomorphic family of relations, resolvent convergence.

UDC: 517.983

Received: 22.01.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:2, 13–24

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