In this work, using the Calkin-Gorbachuk method firstly all selfadjoint extensions of theminimal operator generated by first order linear singular quasi-differential expressionin 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.
📌 3 Maddede Bu Makale
🎯
Amaç & Hipotez:In this work, using the Calkin-Gorbachuk method firstly all selfadjoint extensions of theminimal operator generated by first order linear singular quasi-differential expressionin 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.
📊
Temel Bulgular & Veri:In this work, using the Calkin-Gorbachuk method firstly all selfadjoint extensions of theminimal operator generated by first order linear singular quasi-differential expressionin 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.
💡
Sonuç & Katkı:In this work, using the Calkin-Gorbachuk method firstly all selfadjoint extensions of theminimal operator generated by first order linear singular quasi-differential expressionin 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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
In this work, using the Calkin-Gorbachuk method firstly all selfadjoint extensions of theminimal operator generated by first order linear singular quasi-differential expressionin 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.
🔖
Bu Makaleye Atıf Yap
AL, P. İ., ISMAİLOV, Z. I. (2022). Selfadjoint Singular Quasi-Differential Operators of First Order. Hittite Journal of Science and Engineering, Cilt: 6 - Sayı: 1, 31–35. https://ajindex.com/articles/537994
Bairamov E, Öztürk Mert R, Ismailov Z. Selfadjoint extensions of a singular differential operator. Journal of Mathematical Chemistry 50 (2012) 1100-1110
El-Gebeily MA, O'Regan D, Agarwal R. Characterization of self-adjoint ordinary differential operators. Mathematical and Computer Modelling 54 (2011) 659-672
Everitt WN, Markus L. The Glazman-Krein-Naimark Theorem for ordinary differential operators. Operator Theory, Advances and Applications 98 (1997) 118-130
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
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)
Gorbachuk VI, Gorbachuk MI. Boundary Value Problems for Operator Differential Equations, Mathematics and its Applications, Kluwer, Dordrecht, 1991
Hörmander L. On the theory of general partial differential operators. Acta Mathematica 94 (1955) 161-248
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
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
Naimark MA. Linear Differential Operators II, NewYork, Ungar, 1968
Rofe-Beketov FS, Kholkin AM. Spectral Analysis of Differential Operators, World Scientific Monograph Series in Mathematics 7, USA, 2005
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
Zettl A, Sun J. Survey Article: Self-adjoint ordinary differential operators and their spectrum. Rosky Mountain Journal of Mathematics 45 1 (2015) 763-886.