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Year 2019, , 31 - 35, 28.03.2019
https://doi.org/10.17350/HJSE19030000130

Abstract

References

  • 1. Bairamov E, Öztürk Mert R, Ismailov Z. Selfadjoint extensions of a singular differential operator. Journal of Mathematical Chemistry 50 (2012) 1100-1110.
  • 2. El-Gebeily MA, O'Regan D, Agarwal R. Characterization of self-adjoint ordinary differential operators. Mathematical and Computer Modelling 54 (2011) 659-672.
  • 3. Everitt WN, Markus L. The Glazman-Krein-Naimark Theorem for ordinary differential operators. Operator Theory, Advances and Applications 98 (1997) 118-130.
  • 4. Everitt WN, Poulkou A. Some observations and remarks on differential operators generated by first order boundary value problems. Journal of Computational and Applied Mathematics 153 (2003) 201-211.
  • 5. Glazman IM. On the theory of singular differential operators Uspekhi Matematicheskikh Nauk 40 (1962) 102-135, ( English translation in American Mathematical Society Translations 4 (1962) 331-372).
  • 6. Gorbachuk VI, Gorbachuk MI. Boundary Value Problems for Operator Differential Equations, Mathematics and its Applications, Kluwer, Dordrecht, 1991.
  • 7. Hörmander L. On the theory of general partial differential operators. Acta Mathematica 94 (1955) 161-248.
  • 8. Ismailov ZI, Öztürk Mert R. Selfadjoint extensions of a singular multipoint differential operator of first Order. Electronic Journal of Differential Equations 129 (2013) 1-11.
  • 9. Ismailov ZI, Yılmaz B, Öztürk Mert R. On the spectrum of some class of selfadjoint singular differential operators. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 65 (2016) 137-145.
  • 10. Naimark MA. Linear Differential Operators II, NewYork, Ungar, 1968.
  • 11. Rofe-Beketov FS, Kholkin AM. Spectral Analysis of Differential Operators, World Scientific Monograph Series in Mathematics 7, USA, 2005.
  • 12. Stone MH. Linear Transformations in Hilbert Space and Their Applications in Analysis, American Mathematical Society Colloquium Publications 15, USA, 1932.
  • 13. von Neumann J. Allgemeine eigenwerttheories hermitescher funktionaloperatoren. Mathematische Annalen 102 (1929-1930) 49-31.
  • 14. Zettl A, Sun J. Survey Article: Self-adjoint ordinary differential operators and their spectrum. Rosky Mountain Journal of Mathematics 45 1 (2015) 763-886.

Selfadjoint Singular Quasi-Differential Operators for First Order

Year 2019, , 31 - 35, 28.03.2019
https://doi.org/10.17350/HJSE19030000130

Abstract

I n this work, using the Calkin-Gorbachuk method firstly all selfadjoint extensions of the minimal operator generated by first order linear singular quasi-differential expression in the weighted Hilbert space of vector-functions on right semi-axis have been described. Lastly, the structure of the spectrum set of these extensions has been investigated

References

  • 1. Bairamov E, Öztürk Mert R, Ismailov Z. Selfadjoint extensions of a singular differential operator. Journal of Mathematical Chemistry 50 (2012) 1100-1110.
  • 2. El-Gebeily MA, O'Regan D, Agarwal R. Characterization of self-adjoint ordinary differential operators. Mathematical and Computer Modelling 54 (2011) 659-672.
  • 3. Everitt WN, Markus L. The Glazman-Krein-Naimark Theorem for ordinary differential operators. Operator Theory, Advances and Applications 98 (1997) 118-130.
  • 4. Everitt WN, Poulkou A. Some observations and remarks on differential operators generated by first order boundary value problems. Journal of Computational and Applied Mathematics 153 (2003) 201-211.
  • 5. Glazman IM. On the theory of singular differential operators Uspekhi Matematicheskikh Nauk 40 (1962) 102-135, ( English translation in American Mathematical Society Translations 4 (1962) 331-372).
  • 6. Gorbachuk VI, Gorbachuk MI. Boundary Value Problems for Operator Differential Equations, Mathematics and its Applications, Kluwer, Dordrecht, 1991.
  • 7. Hörmander L. On the theory of general partial differential operators. Acta Mathematica 94 (1955) 161-248.
  • 8. Ismailov ZI, Öztürk Mert R. Selfadjoint extensions of a singular multipoint differential operator of first Order. Electronic Journal of Differential Equations 129 (2013) 1-11.
  • 9. Ismailov ZI, Yılmaz B, Öztürk Mert R. On the spectrum of some class of selfadjoint singular differential operators. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 65 (2016) 137-145.
  • 10. Naimark MA. Linear Differential Operators II, NewYork, Ungar, 1968.
  • 11. Rofe-Beketov FS, Kholkin AM. Spectral Analysis of Differential Operators, World Scientific Monograph Series in Mathematics 7, USA, 2005.
  • 12. Stone MH. Linear Transformations in Hilbert Space and Their Applications in Analysis, American Mathematical Society Colloquium Publications 15, USA, 1932.
  • 13. von Neumann J. Allgemeine eigenwerttheories hermitescher funktionaloperatoren. Mathematische Annalen 102 (1929-1930) 49-31.
  • 14. Zettl A, Sun J. Survey Article: Self-adjoint ordinary differential operators and their spectrum. Rosky Mountain Journal of Mathematics 45 1 (2015) 763-886.
There are 14 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Pembe Ipek Al This is me

Zameddin Ismailov This is me

Publication Date March 28, 2019
Published in Issue Year 2019

Cite

Vancouver Al PI, Ismailov Z. Selfadjoint Singular Quasi-Differential Operators for First Order. Hittite J Sci Eng. 2019;6(1):31-5.

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