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ЖУРНАЛЫ // Журнал математической физики, анализа, геометрии // Архив

Журн. матем. физ., анал., геом., 2009, том 5, номер 2, страницы 123–144 (Mi jmag121)

Эта публикация цитируется в 3 статьях

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

Аннотация: 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.

Ключевые слова и фразы: linear relation, symmetric relation, spectrum, generalized resolvent, holomorphic operator function, differential elliptic-type expres-sion, Green function, Banach space, Hilbert space.

MSC: 47A06, 47A10, 34B05

Поступила в редакцию: 28.10.2007

Язык публикации: английский



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