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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2008 Number 11, Pages 12–26 (Mi ivm1773)

This article is cited in 2 papers

Generalized resolvents of linear relations generated by a nonnegative operator function and a differential elliptic-type expression

V. M. Bruk

Saratov State Technical University

Abstract: We study invertible extensions of the minimal relation generated by a nonnegative operator function and a differential elliptic-type expression. We prove that the operators inverse to such extensions are integral operators and describe such integral operators. We obtain a formula for generalized resolvents of the minimal relation.

Keywords: linear relation, symmetric relation, generalized resolvent, Green function, operator function.

UDC: 517.983

Received: 31.08.2006


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2008, 52:11, 10–22

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© Steklov Math. Inst. of RAS, 2025