On Linear Relations Generated by an Integro-Differential Equation with Nevanlinna Measure in the Infinite-Dimensional Case

V. M. Bruk

Saratov State Technical University

Abstract: A system of integral equations that can be reduced to an integro-differential equation with Nevanlinna measure is considered. The families of maximal and minimal linear relations are defined and their holomorphy is established. It is proved that the operators inverse to continuously invertible restrictions of the maximal relations are integral.

Keywords: integro-differential equation, Nevanlinna measure, maximal (minimal) linear relation, holomorphy, separable Hilbert space, Krein–Feller differential operation, Lebesgue–Stieltjes integral.

UDC: 517.983

Received: 17.03.2013
Revised: 25.08.2013

DOI: 10.4213/mzm10284

 English version: Mathematical Notes, 2014, 96:1, 10–25

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