Investigation of the spectral properties of a fourth order differential operator with finite transmission conditions

Investigation of the spectral properties of a fourth order differential operator with finite transmission conditions

In this paper, the spectral analysis of a singular dissipative fourth order differential operator in lim‐4 case with finite transmission conditions is investigated. For this purpose, the inverse operator with explicit form is used. Finally, with the help of Livšic's theorem, it is proved that a...

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Veröffentlicht in:Mathematical methods in the applied sciences 2016-04, Vol.39 (6), p.1298-1310
1. Verfasser: Uurlu, Ekin
Format: Artikel
Sprache:eng
Schlagworte:
completeness theorem
Dissipation
dissipative operators
fourth order operator
Inverse
Mathematical analysis
Operators
Operators (mathematics)
Roots
Spectra
transmission conditions
Vectors (mathematics)
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Zusammenfassung:In this paper, the spectral analysis of a singular dissipative fourth order differential operator in lim‐4 case with finite transmission conditions is investigated. For this purpose, the inverse operator with explicit form is used. Finally, with the help of Livšic's theorem, it is proved that all root vectors of the fourth order dissipative operator in lim‐4 case with finite transmission conditions are complete in the Hilbert space. Copyright © 2015 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3550