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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2018 / Volume: 67 Issue: 2

SELFADJOINT SINGULAR DIFFERENTIAL OPERATORS FOR FIRST ORDER

Pembe İpek
İ.zameddin Ismaılov
Sayfa
—
Yayın Tarihi
2018-08-01
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, the structure of spectrum set of such extensions is researched

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The parametrization of all selfadjoint extensions of the minimal operator generated by frst order linear symmetric singular differential-operator expression in the Hilbert space of vector-functions defined at the right semi-axis has been given.
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Temel Bulgular & Veri:To this end we use the Calkin-Gorbachuk method.
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Sonuç & Katkı:Finally, the structure of spectrum set of such extensions is researched
🔬Tür:Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

The parametrization of all selfadjoint extensions of the minimal operator generated by frst order linear symmetric singular differential-operator expression in the Hilbert space of vector-functions defined at the right semi-axis has been given. To this end we use the Calkin-Gorbachuk method. Finally, the structure of spectrum set of such extensions is researched

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Bu Makaleye Atıf Yap

İpek, P., Ismaılov, İ. (2018). SELFADJOINT SINGULAR DIFFERENTIAL OPERATORS FOR FIRST ORDER. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 67 Issue: 2. https://ajindex.com/articles/1470054

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Kaynakça (17)

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  3. Everitt, W.N., Markus, L., The Glazman-Krein-Naimark Theorem for ordinary diğerential operators. Operator Theory, Advances and Applications, (1997); 98: 118-130.
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  5. Glazman, I.M., On the theory of singular diğerential operators. Uspehi Math Nauk (1962);: 102-135,(English translation in Amer Math Soc Translations (1) 1962; 4: 331-372).
  6. Gorbachuk, V.I. and Gorbachuk M.I., Boundary Value Problems for Operator Diğerential Equations. Kluwer, Dordrecht: 1991.
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  8. Naimark, M.A., Linear Diğerential Operators II. NewYork, Ungar, 1968.
  9. Rofe-Beketov, F.S. and Kholkin, A.M., Spectral analysis of diğerential operators. World Scienti…c Monograph Series in Mathematics 7, 2005.
  10. Stone, M.H., Linear transformations in Hilbert space and their applications in analysis. Amer. Math. Soc. Collog. Publications (1932); 15: 49-31. von Neumann, J., Allgemeine eigenwerttheories hermitescher funktionaloperatoren. Math. Ann. (1929 );102: 49-31.
  11. Zettl, A and Sun, J., Survey Article: Self-Adjoint ordinary diğerential operators and their spectrum. Roky Mountain Journal of Mathematics (2015); 45,1: 763-886.
  12. Current address: Pembe IPEK: Institute of Natural Sciences, Karadeniz Technical University,, Trabzon, Turkey E-mail address: [email protected] ORCID Address: Current address: Zameddin I. ISMAILOV: Institute of Natural Sciences, Karadeniz Technical University, 61080, Trabzon, Turkey
  13. El-Gebeily, M.A., O’ Regan, D. and Agarwal R., Characterization of self-adjoint ordinary diğerential operators. Mathematical and Computer Modelling (2011); 54, 659-672.
  14. Glazman, I.M., On the theory of singular diğerential operators. Uspehi Math Nauk (1962);: 102-135,(English translation in Amer Math Soc Translations (1) 1962; 4: 331-372).
  15. Stone, M.H., Linear transformations in Hilbert space and their applications in analysis. Amer. Math. Soc. Collog. Publications (1932); 15: 49-31. von Neumann, J., Allgemeine eigenwerttheories hermitescher funktionaloperatoren. Math. Ann. (1929 );102: 49-31.
  16. Zettl, A and Sun, J., Survey Article: Self-Adjoint ordinary diğerential operators and their spectrum. Roky Mountain Journal of Mathematics (2015); 45,1: 763-886.
  17. Current address: Pembe IPEK: Institute of Natural Sciences, Karadeniz Technical University,, Trabzon, Turkey E-mail address: [email protected] ORCID Address: Current address: Zameddin I. ISMAILOV: Institute of Natural Sciences, Karadeniz Technical University, 61080, Trabzon, Turkey