Coordinate-Free Approach for the Model Operator Associated With a Third-Order Dissipative Operator

In this paper we investigate the spectral properties of a third-order differential operator generated by a formally-symmetric differential expression and maximal dissipative boundary conditions. In fact, using the boundary value space of the minimal operator we introduce maximal selfadjoint and maxi...

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Bibliographic Details
Published inFrontiers in physics Vol. 7
Main Authors Uğurlu, Ekin, Baleanu, Dumitru
Format Journal Article
LanguageEnglish
Published Frontiers Media S.A 10.07.2019
Subjects
characteristic function
coordinate-free approach
dissipative operator
model operator
spectral analysis
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ISSN2296-424X
2296-424X
DOI10.3389/fphy.2019.00099

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Summary:In this paper we investigate the spectral properties of a third-order differential operator generated by a formally-symmetric differential expression and maximal dissipative boundary conditions. In fact, using the boundary value space of the minimal operator we introduce maximal selfadjoint and maximal non-selfadjoint (dissipative, accumulative) extensions. Using Solomyak's method on characteristic function of the contractive operator associated with a maximal dissipative operator we obtain some results on the root vectors of the dissipative operator. Finally, we introduce the selfadjoint dilation of the maximal dissipative operator and incoming and outgoing eigenfunctions of the dilation.2000 Mathematics Subject Classification: Primary 47A45, 47E05; Secondary 47A20
ISSN:2296-424X
2296-424X
DOI:10.3389/fphy.2019.00099