Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2009, Volume 5, Number 2, Pages 123–144 (Mi jmag121)  
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
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Abstract: 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.
Received: 28.10.2007
Bibliographic databases:
Document Type: Article
MSC: 47A06, 47A10, 34B05
Language: English
Citation: 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
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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