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Mathematical Problems in Engineering
Volume 2014, Article ID 350651, 6 pages
http://dx.doi.org/10.1155/2014/350651
Research Article

On Certain Aspects of the Multidimensional -Spectral Theory

Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania

Received 10 August 2014; Accepted 1 December 2014; Published 28 December 2014

Academic Editor: Kishin Sadarangani

Copyright © 2014 Cristina Serbanescu and Ioan Bacalu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper has two parts. The first one provides the preliminary notions introducing certain general concepts, in order to study, in the second part, the properties of some operator systems which admit spectral residual decompositions, -decomposable, -spectral, and -scalar systems, and so forth. The results obtained by Frunză, 1975, are generalized, taking the results of Foias, 1963, as a model and adopting them.