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

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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.

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Authors and Affiliations

  1. Saratov State Technical University, ul. Politekhnicheskaya 77, Saratov, 410054, Russia

    V. M. Bruk

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  1. V. M. Bruk
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Correspondence to V. M. Bruk.

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Original Russian Text © V.M. Bruk, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 11, pp. 12–26.

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Bruk, V.M. Generalized resolvents of linear relations generated by a nonnegative operator function and a differential elliptic-type expression. Russ Math. 52, 10–22 (2008). https://doi.org/10.3103/S1066369X08110029

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  • DOI: https://doi.org/10.3103/S1066369X08110029

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