This article is cited in 4 papers

On Invertible Contractions of Quotients Generated by a Differential Expression and by a Nonnegative Operator Function

V. M. Bruk

Saratov State Technical University

Abstract: In the present paper, we describe invertible contractions of the maximal quotient generated by a differential expression with bounded operator coefficients and by a nonnegative operator function. We show that the operators inverse to such contractions are integral operators and prove a criterion for such operators to be holomorphic. Using the results obtained, we describe the generalized resolvents of symmetric quotients.

Keywords: invertible contraction, integral operator, holomorphic operator, operator function, Hilbert space, self-adjoint operator, Borel measurable function.

UDC: 517.983.53

Received: 15.04.2005
Revised: 17.03.2007

DOI: 10.4213/mzm4080

 English version: Mathematical Notes, 2007, 82:5, 583–595

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