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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| Published in | Frontiers in physics Vol. 7 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Frontiers Media S.A
10.07.2019
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| Online Access | Get full text |
| ISSN | 2296-424X 2296-424X |
| DOI | 10.3389/fphy.2019.00099 |
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| Abstract | 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 |
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| AbstractList | 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 |
| Author | Uğurlu, Ekin Baleanu, Dumitru |
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| References_xml | – volume-title: Harmonic Analysis of Operators on Hilbert Space, Revised and Enlarged Edition year: 2010 ident: B18 doi: 10.1007/978-1-4419-6094-8 – volume-title: Operators, Functions, and Systems: An Easy Reading, Vol. 2. Model Operators and Systems year: 2002 ident: B17 – volume: 178 start-page: 57 year: 1989 ident: B5 article-title: Functional model for dissipative operators. A coordinate-free approach, Journal of Soviet Mathematics 61 (1992), 1981–2002; Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A publication-title: Steklova Akademii Nauk SSSR. – volume: 41 start-page: 1404 year: 2017 ident: B10 article-title: Dissipative operator and its Cayley transform publication-title: Turk J Math. doi: 10.3906/mat-1610-83 – volume-title: Harmonic Analysis of Operators on Hilbert Space year: 1970 ident: B1 – volume-title: Linear Differential Operators year: 1968 ident: B14 – volume: 37 start-page: 372 year: 1962 ident: B9 article-title: Self-adjoint boundary value problems on finite intervals publication-title: J Lond Math Soc. doi: 10.1112/jlms/s1-37.1.372 – year: 1974 ident: B19 article-title: Indefinite Inner Product Spaces doi: 10.1007/978-3-642-65567-8 – volume: 10 start-page: 5999 year: 2017 ident: B11 article-title: On a completely non-unitary contraction and associated dissipative difference operator publication-title: J Nonlinear Sci Appl. doi: 10.22436/jnsa.010.11.36 – volume-title: Scattering Theory year: 1967 ident: B3 – volume-title: Theory of Ordinary Differential Equations year: 1955 ident: B6 – volume-title: Linear Differential Operators Part I: Elementary Theory of Linear Differential Operators year: 1966 ident: B8 – volume-title: Linear Operators Part II: Spectral Theory year: 1963 ident: B7 – volume-title: Bull Malays Math Sci Soc year: 2018 ident: B12 article-title: Extensions of a minimal third-order formally symmetric operator doi: 10.1007/s40840-018-0696-8 – volume: 8 start-page: 627 year: 1978 ident: B15 article-title: Deficiency indices of odd-order differential operators publication-title: Rocky Moun J Math. doi: 10.1216/RMJ-1978-8-4-627 – volume-title: Boundary Value Problems for Ordinary Differential Equations year: 1991 ident: B16 doi: 10.1007/978-94-011-3714-0 – start-page: 405 volume-title: The Gohberg Anniversary Collection. Operator Theory: Advances and Applications year: 1989 ident: B4 article-title: A Unified approach to function models, and the transcription problem doi: 10.1007/978-3-0348-9278-0_23 – volume: 26 start-page: 289 year: 1965 ident: B2 article-title: On spectral sets having connected complement publication-title: Acta Sci Math. – volume: 343 start-page: 247 year: 2019 ident: B13 article-title: Regular third-order boundary value problems publication-title: Appl Math Comput. doi: 10.1016/j.amc.2018.09.046 |
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| Title | Coordinate-Free Approach for the Model Operator Associated With a Third-Order Dissipative Operator |
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