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http://dx.doi.org/10.5831/HMJ.2022.44.4.485

SPECTRAL EXPANSION FOR DISCONTINUOUS SINGULAR DIRAC SYSTEMS  

Bilender P., Allahverdiev (Department of Mathematics, Suleyman Demirel University)
Huseyin, Tuna (Department of Mathematics, Mehmet Akif Ersoy University)
Publication Information
Honam Mathematical Journal / v.44, no.4, 2022 , pp. 485-503 More about this Journal
Abstract
In this work, a discontinuous singular Dirac system is studied. For this system, a spectral function is constructed. Finally, by using the spectral function, a spectral expansion formula is given.
Keywords
Dirac system; impulsive condition; Green's matrix; spectral function; spectral expansion;
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1 B. P. Allahverdiev and H. Tuna, Spectral expansion for the singular Dirac system with impulsive conditions, Turkish J. Math. 42 (2018), 2527-2545.   DOI
2 B. P. Allahverdiev and H. Tuna, Spectral expansion for singular conformable fractional Dirac systems, Rend. Circ. Mat. Palermo II. Ser. 69 (2020) 1359-1372.   DOI
3 B. P. Allahverdiev and H. Tuna, Resolvent operator of singular dirac system with transmission conditions, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 23 (2019), no. 538, 85-105.   DOI
4 B. P. Allahverdiev and H. Tuna, Eigenfunction expansion in the singular case for Dirac systems on time scales, Konuralp J. Math. 7 (2019), no. 1, 128-135.
5 B. P. Allahverdiev and H. Tuna, On expansion in eigenfunction for Dirac systems on the unbounded time scales, Differ. Equ. Dyn. Syst. 30 (2022), 271-285.   DOI
6 B. P. Allahverdiev and H. Tuna, The Parseval equality and expansion formula for singular Hahn-Dirac system. In S. Alparslan Gok, & D. Arugaslan Cincin (Ed.), Emerging Applications of Differential Equations and Game Theory (pp. 209-235), IGI Global, 2020.
7 I. Dehghani and A. J. Akbarfam, Resolvent operator and self-adjointness of SturmLiouville operators with a finite number of transmission conditions, Mediterr. J. Math. 11 (2014), no. 2, 447-462.   DOI
8 S. Faydaoglu and G. Sh. Guseinov, An expansion result for a Sturm-Liouville eigenvalue problem with impulse, Turkish J. Math. 34 (2010), no. 3, 355-366.
9 B. Keskin and A. S. Ozkan, Inverse spectral problems for Dirac operator with eigenvalue dependent boundary and jump conditions, Acta Math. Hungarica 130 (2011), 309-320.   DOI
10 A. N. Kolmogorov and S. V. Fomin, Introductory Real Analysis, Translated by R.A. Silverman, Dover Publications, New York, 1970.
11 F. R. Lapwood and T. Usami, Free Oscillations of the Earth, Cambridge University Press, Cambridge, 1981.
12 B. M. Levitan and I. S. Sargsjan, Sturm-Liouville and Dirac Operators, Mathematics and its Applications (Soviet Series), Kluwer Academic Publishers Group, Dordrecht, 1991.
13 K. Li, J. Sun, and X. Hao, Weyl function of Sturm-Liouville problems with transmission conditions at finite interior points, Mediter. J. Math. 14 (2017), no. 189, 1-15.   DOI
14 A. V. Likov and Yu. A. Mikhailov, The Theory of Heat and Mass Transfer, Translated from Russian by I. Shechtman, Israel Program for Scientific Translations, Jerusalem, 1965.
15 O. N. Litvinenko and V. I. Soshnikov, The Theory of Heteregenous Lines and their Applications in Radio Engineering, Radio, Moscow 1964 (in Russian).
16 R. K. Mamedov and O. Akcay, Inverse eigenvalue problem for a class of Dirac operators with discontinuous coefficient, Bound. Value Probl. 2014 (2014), no. 110, 1-20.   DOI
17 O. Sh. Mukhtarov, H. Olgar, and K. Aydemir, Resolvent operator and spectrum of new type boundary value problems, Filomat 29 (2015), no. 7, 1671-1680.   DOI
18 O. Sh. Mukhtarov, Discontinuous boundary-value problem with spectral parameter in boundary conditions, Turkish J. Math. 18 (1994), 183-192.
19 M. A. Naimark, Linear differential operators, 2nd edn, Nauka, Moscow, 1969; English Transl. of 1st Ed., Parts 1 and 2, Ungar, New York, 1967 and 1968.
20 B. Thaller, The Dirac Equation, Springer, Berlin Heidelberg, 1992.
21 E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Part I, Second Edition, Clarendon Press, Oxford, 1962.
22 C. F. Yang and G. L. Yuan, Determination of Dirac operator with eigenvalue-dependent boundary and jump conditions, Appl. Anal. 94 (2015), no. 7, 1460-1478.   DOI
23 A. Zettl, Adjoint and self-adjoint boundary value problems with interface conditions, SIAM J. Appl. Math. 16 (1968), no. 4, 851-859.    DOI