This article is cited in 5 papers

Linear relations generated by an integral equation with Nevanlinna operator measure

V. M. Bruk

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

Abstract: We define families of maximal and minimal linear relations generated by an integral equation with Nevanlinna operator measure and prove their holomorphic property. We also prove that if a restriction of a maximal relation is continuously invertible, then the operator inverse to this restriction is integral. We apply the obtained results for proving the constancy of deficient numbers of some integral and differential equations.

Keywords: Hilbert space, linear relation, integral equation, holomorphic family of relations, deficient number.

UDC: 517.983

Received: 30.08.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:10, 1–14

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