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Journals / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 2

Dissipative canonical type differential operators for first order

Rukiye Öztürk MERT
Zameddin İSMAİLOV
Pembe İpek AL
Pages
481–490
Publication Date
2020-03-01
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Also, the spectrum set of these extensions has been investigated.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, using the Calkin-Gorbachuk method, the general form of all maximally dissipative extensions of the minimal operator generated by the first order linear symmetric canonical type quasi-differential expression in the weighted Hilbert space of vector functions has been found.
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Key Findings & Data:In this paper, using the Calkin-Gorbachuk method, the general form of all maximally dissipative extensions of the minimal operator generated by the first order linear symmetric canonical type quasi-differential expression in the weighted Hilbert space of vector functions has been found.
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Conclusion & Impact:Also, the spectrum set of these extensions has been investigated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Dissipative operator · quasi-differential operator · spectrum

Abstract

In this paper, using the Calkin-Gorbachuk method, the general form of all maximally dissipative extensions of the minimal operator generated by the first order linear symmetric canonical type quasi-differential expression in the weighted Hilbert space of vector functions has been found. Also, the spectrum set of these extensions has been investigated.

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Cite This Article

MERT, R. Ö., İSMAİLOV, Z., AL, P. İ. (2020). Dissipative canonical type differential operators for first order. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 2, 481–490. https://ajindex.com/articles/185560

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References (11)

  1. Behrndt J, Hassi S, Snoo H, Wietsma R. Square-integrable solutions and Weyl functions for singular canonical systems. Mathematische Nachrichten 2001; 284: 1334-1384
  2. Behrndt J, Malamud M, Neidhardt H. Scattering theory for open quantum systems with finite rank coupling. Mathematical Physics, Analysis and Geometry 2007; 10: 313-358
  3. Derkach V, Malamud M. Generalized resolvents and the boundary value problems for Hermitian operators with gaps. Journal of Functional Analysis 1991; 95: 1-95
  4. Derkach V, Malamud M. The extension theory of Hermitian operators and the moment problem. Journal of Mathematical Sciences 1995; 73: 141-242
  5. Fischbacher C. On the theory of dissipative extensions. PhD, University of Kent School of Mathematics, Canterbury, England, 2017
  6. Gorbachuk VI, Gorbachuk ML. Boundary Value Problems for Operator Differential Equations. 1st ed. Dordrecht, the Netherlands: Kluwer Academic Publishers, 1991
  7. Hörmander L. On the theory of general partial differential operators. Acta Mathematica 1955; 94: 161-248
  8. Mogilevskii V. Boundary pairs and boundary conditions for general (not necessarily definite) first-order symmetric system with arbitrary deficiency indices. Mathematische Nachrichten 2012; 285: 1895-1931
  9. Nagy BSz, Foias C. Analyse Harmonique des Operateurs de L’ espace de Hilbert. Paris, France: Budapest Akadémiai Kiadó, 1967
  10. Naimark MA. Linear Differential Operators. New York, USA: Frederick Ungar Publishing Company, 1968
  11. Rofe-Beketov FS, Kholkin AM. Spectral analysis of differential operators. World Scientific Monograph Series in Mathematics 7; 2005. [12] von Neumann J. Allgemeine eigenwerttheories hermitescher funktionaloperatoren. Mathematische Annalen 1929- 1930; 102: 49-131 (article in German)