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dc.contributor.authorSokolov, Maksim S. ( )
dc.date.accessioned2020-11-25T20:21:33Z
dc.date.available2020-11-25T20:21:33Z
dc.date.issued2003-07-10
dc.identifier.citationSokolov, M. S. (2003). An abstract approach to some spectral problems of direct sum differential operators. Electronic Journal of Differential Equations, 2003(75), pp. 1-6.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13015
dc.description.abstractIn this paper, we study the common spectral properties of abstract self-adjoint direct sum operators, considered in a direct sum Hilbert space. Applications of such operators arise in the modelling of processes of multi-particle quantum mechanics, quantum field theory and, specifically, in multi-interval boundary problems of differential equations. We show that a direct sum operator does not depend in a straightforward manner on the separate operators involved. That is, on having a set of self-adjoint operators giving a direct sum operator, we show how the spectral representation for this operator depends on the spectral representations for the individual operators (the coordinate operators) involved in forming this sum operator. In particular it is shown that this problem is not immediately solved by taking a direct sum of the spectral properties of the coordinate operators. Primarily, these results are to be applied to operators generated by a multi-interval quasi-differential system studied, in the earlier works of Ashurov, Everitt, Gesztezy, Kirsch, Markus and Zettl. The abstract approach in this paper indicates the need for further development of spectral theory for direct sum differential operators.en_US
dc.formatText
dc.format.extent6 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectDirect sum operatorsen_US
dc.subjectCyclic vectoren_US
dc.subjectSpectral representationen_US
dc.subjectUnitary transformationen_US
dc.titleAn abstract approach to some spectral problems of direct sum differential operatorsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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