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Dec 2003 ON SOME SPECTRAL PROPERTIES OF OPERATORS GENERATED BY QUASI-DIFFERENTIAL MULTI-INTERVAL SYSTEMS
MAKSIM SOKOLOV
Methods Appl. Anal. 10(4): 513-532 (Dec 2003).

Abstract

We construct the common and the ordered spectral representation for operators, generated as direct sums of self-adjoint extensions of quasi-differential minimal operators on a multiinterval set (self-adjoint vector-operators), acting in a Hilbert space. The structure of the ordered representation is investigated for the case of differential coordinate operators. Results, connected with other spectral properties of such vector-operators, such as the introduction of the identity resolution and the spectral multiplicity have also been obtained. Vector-operators have been mainly studied by W.N. Everitt, L. Markus and A. Zettl. Being a natural continuation of Everitt-Markus-Zettl theory, the presented results reveal the internal structure of self-adjoint differential vector-operators and are essential for the further study of their spectral properties.

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MAKSIM SOKOLOV. "ON SOME SPECTRAL PROPERTIES OF OPERATORS GENERATED BY QUASI-DIFFERENTIAL MULTI-INTERVAL SYSTEMS." Methods Appl. Anal. 10 (4) 513 - 532, Dec 2003.

Information

Published: Dec 2003
First available in Project Euclid: 20 August 2004

zbMATH: 1078.34066
MathSciNet: MR2105037

Rights: Copyright © 2003 International Press of Boston

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Vol.10 • No. 4 • Dec 2003
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