This article is cited in 3 scientific papers (total in 3 papers)
On linear relations generated by nonnegative operator function and degenerate elliptic differential-operator expression
V. M. Bruk
Saratov State Technical University, 77 Politekhnitcheskaja Str., Saratov, 410054, Russia
In terms of boundary values, we describe a spectrum of the linear relations indicated in the paper title. We study the invertible restrictions of maximal relation and show that the operators inverse to these restrictions are integral. The criterion of holomorphicity of the family of these operators is determined. Using the results obtained, we show that the minimal relation is symmetric in Hilbert space and describe all generalized resolvents of this relation.
Key words and phrases:
linear relation, symmetric relation, spectrum, generalized resolvent, holomorphic operator function, differential elliptic-type expres-sion, Green function, Banach space, Hilbert space.
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MSC: 47A06, 47A10, 34B05
V. M. Bruk, “On linear relations generated by nonnegative operator function and degenerate elliptic differential-operator expression”, Zh. Mat. Fiz. Anal. Geom., 5:2 (2009), 123–144
Citation in format AMSBIB
\paper On linear relations generated by nonnegative operator function and degenerate elliptic differential-operator expression
\jour Zh. Mat. Fiz. Anal. Geom.
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This publication is cited in the following articles:
V. M. Bruk, “On Linear Relations Generated by an Integro-Differential Equation with Nevanlinna Measure in the Infinite-Dimensional Case”, Math. Notes, 96:1 (2014), 10–25
V. M. Bruk, “Boundary value problems for integral equations with operator measures”, Probl. anal. Issues Anal., 6(24):1 (2017), 19–40
V. M. Bruk, “On self-adjoint and invertible linear relations generated by integral equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 1, 106–121
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