SELFADJOINT SINGULAR DIFFERENTIAL OPERATORS FOR FIRST ORDER

Year 2018, Volume: 67 Issue: 2, 156 - 164, 01.08.2018

Pembe İpek İ.zameddin Ismaılov

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

References

• Bairamov, E., Öztürk, M.R. and Ismailov, Z., Selfadjoint extensions of a singular diğerential operator. J. Math. Chem. (2012), 50, 1100-1110.
• 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.
• Everitt, W.N., Markus, L., The Glazman-Krein-Naimark Theorem for ordinary diğerential operators. Operator Theory, Advances and Applications, (1997); 98: 118-130.
• Everitt, W.N. and Poulkou, A., Some observations and remarks on diğerential operators generated by …rst order boundary value problems. Journal of Computational and Applied Mathematics (2003), 153: 201-211.
• 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).
• Gorbachuk, V.I. and Gorbachuk M.I., Boundary Value Problems for Operator Diğerential Equations. Kluwer, Dordrecht: 1991.
• Hörmander, L., On the theory of general partial diğerential operators. Acta Mathematica (1955), 94: 161-248.
• Naimark, M.A., Linear Diğerential Operators II. NewYork, Ungar, 1968.
• Rofe-Beketov, F.S. and Kholkin, A.M., Spectral analysis of diğerential operators. World Scienti…c Monograph Series in Mathematics 7, 2005.
• 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.
• 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.
• Current address : Pembe IPEK: Institute of Natural Sciences, Karadeniz Technical University, , Trabzon, Turkey E-mail address : [e-mail] ORCID Address: Current address : Zameddin I. ISMAILOV: Institute of Natural Sciences, Karadeniz Technical University, 61080, Trabzon, Turkey