İ.zameddin ISMAILOV, Bülent YILMAZ, Rukiye ÖZTÜRK MERT

On the spectrums of some class of selfadjoint singular differential operators

In this work, based on the Everitt-Zettl and Calkin-Gorbachuk methods in terms of boundary values all self adjoint extensions of the minimal operator generated by some linear singular multipoint symmetric differential operator expression for first order in the direct sum of Hilbert spaces of vector functions on the right semi-axis are described. Later structure of the spectrumof these extensions is investigated

Keywords:

Everitt-Zettl and Calkin-Gorbachuk methods, singular multipoint diğerential operators, selfadjoint extension, spectrum,

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J.von Neumann, Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren, Math. Ann., 1929-1930, 102, p.49-131.
N. Dunford, J. T. Schwartz, Linear Operators I; II, Second ed., Interscience, New York, 1958
V. I. Gorbachuk, M. L. Gorbachuk, Boundary value problems for operator-diğerential equa- tions, First ed., Kluwer Academic Publisher, Dordrecht, 1991.
F.S. Rofe-Beketov, A.M. Kholkin, Spectral Analysis of Diğerential Operators, World Scien- ti…c Monograph Series in Mathematics, 2005, v.7.
V.I. Gorbachuk, M.L. Gorbachuk, Boundary Value Problems for a First Order Diğerential Operator with Operator Coe¢ cients and Expansion in the Eigen functions of that Equation, Dokl. Akad. Nauk SSSR, 1973, 208, p.1268-1271.
M.A. Naimark, Linear Diğerential Operators, Ungar, New York, 1968.
W.N. Everitt, A. Zettl, Diğerential Operators Generated by a Countable Number of Quasi- Diğerential Expressions on the Real Line, Proc. London Math. Soc., 1992, 64, p.524-544.
A. Zettl, Sturm-Liouville Theory, Amer. Math. Soc., Mathematical Survey and Monographs, Rhode Island, 2005, v.121.
E. Bairamov, R. Öztürk Mert, Z. Ismailov, Selfadjoint extensions of a singular diğerential operator, J. Math. Chem., 2012, 50, p.1100-1110.
Z. I. Ismailov, Selfadjoint extensions of multipoint singular diğerential operators, Electr. Journal of Diğ . Equat., 2013, no.231, p.1-13.
Z. I. Ismaılov, M. Sertbas, E. Otkun Cevik, Selfadjoint Extentions of a First Order Diğerential Operator, Appl. Math. Inf. Sci. Lett., 2015, 3, no.2, 39-45.
E. Bairamov, M. Sertbas, Z. I. Ismailov, Self-adjoint extensions of singular third-order diğerential operator and applications, AIP Conference Proceeding, 2014, 1611, 177; doi: 1063/1.4893826.
Current address : Zameddin I. ISMAILOV, Department of Mathematics, Faculty of Sciences, Karadeniz Technical University, 61080, Trabzon, Turkey
E-mail address : zameddin.ismailov@gmail.com Current address : Bülent YILMAZ, Department of Mathematics, Marmara University, 34722
Kadıköy Istanbul, Turkey E-mail address : bulentyilmaz@marmara.edu.tr Current address : Rukiye ÖZTÜRK MERT, Department of Mathematics, Art and Science Faculty, Hitit University, 19030, Çorum, Turkey
E-mail address : rukiyeozturkmert@hitit.edu.tr

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics-Cover

ISSN: 1303-5991
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 1948
Yayıncı: Ankara Üniversitesi

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