This article is cited 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

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.

MSC: 47A06, 47A10, 34B05

Received: 28.10.2007

Language: English

Bibliographic databases:

• 
• 
• 
•