Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 7 Sayı: 1, 128 - 135, 15.04.2019

Öz

Kaynakça

  • [1] R. P. Agarwal, M. Bohner and D. O’Regan, Time scale boundary value problems on infinite intervals, J. Comput. Appl. Math., 141 (2002), 27-34.
  • [2] B. P. Allahverdiev and H. Tuna, An expansion theorem for q-Sturm-Liouville operators on the whole line, Turk J Math, 42, (2018), 1060-1071.
  • [3] B. P. Allahverdiev and H. Tuna, Spectral expansion for the singular Dirac system with impulsive conditions, Turk J Math, 42, (2018), 2527 – 2545.
  • [4] D. R. Anderson, G. Sh. Guseinov and J. Hoffacker, Higher-order self-adjoint boundary-value problems on time scales, J. Comput. Appl. Math., 194 (2) (2006) ; 309-342.
  • [5] F. Atici Merdivenci and G. Sh. Guseinov, On Green’s functions and positive solutions for boundary value problems on time scales, J. Comput. Appl. Math., 141 (1-2) (2002); 75-99.
  • [6] M. Bohner and A. Peterson, Dynamic Equations on Time Scales, Birkh¨auser, Boston, 2001.
  • [7] M. Bohner and A. Peterson, (Eds.), Advances in Dynamic Equations on Time Scales, Birkh¨auser, Boston, 2003.
  • [8] T. Gulsen and E. Yilmaz, Spectral theory of Dirac system on time scales, Applicable Analysis, 96(16), (2017), 2684–2694.
  • [9] G. Sh. Guseinov, Self-adjoint boundary value problems on time scales and symmetric Green’s functions, Turkish J. Math., 29 (4); (2005) ; 365􀀀380.
  • [10] G. Sh. Guseinov, Eigenfunction expansions for a Sturm-Liouville problem on time scales. Int. J. Difference Equ. 2 (2007), no. 1, 93–104.
  • [11] G. Sh. Guseinov, An expansion theorem for a Sturm-Liouville operator on semi-unbounded time scales. Adv. Dyn. Syst. Appl. 3 (2008), no. 1, 147–160.
  • [12] S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results Math. 18; (1990); 18􀀀56:
  • [13] G. Hovhannisyan, On Dirac equation on a time scale, Journal of Math. Physics, 52, no.10, 102701, 2011.
  • [14] A. N. Kolmogorov and S. V. Fomin, Introductory Real Analysis. Translated by R.A. Silverman, Dover Publications, New York, 1970.
  • [15] V. Lakshmikantham, S. Sivasundaram and B. Kaymakcalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Dordrecht, 1996.
  • [16] B. M. Levitan and I. S. Sargsjan, Sturm-Liouville and Dirac Operators. Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1991 (translated from the Russian).
  • [17] B. P. Rynne, L2 spaces and boundary value problems on time-scales, J. Math. Anal. Appl. 328; (2007); 1217􀀀1236.
  • [18] B. Thaller, The Dirac Equation, Springer, 1992.
  • [19] E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations. Part I. Second Edition Clarendon Press, Oxford, 1962.
  • [20] J. Weidmann, Spectral Theory of Ordinary Differential Operators, Lecture Notes in Mathematics, 1258, Springer, Berlin 1987.

Eigenfunction Expansion in the Singular Case for Dirac Systems on Time Scales

Yıl 2019, Cilt: 7 Sayı: 1, 128 - 135, 15.04.2019

Öz

In this work, we prove the existence of a spectral function for one dimensional singular Dirac operator on time scales. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.



Kaynakça

  • [1] R. P. Agarwal, M. Bohner and D. O’Regan, Time scale boundary value problems on infinite intervals, J. Comput. Appl. Math., 141 (2002), 27-34.
  • [2] B. P. Allahverdiev and H. Tuna, An expansion theorem for q-Sturm-Liouville operators on the whole line, Turk J Math, 42, (2018), 1060-1071.
  • [3] B. P. Allahverdiev and H. Tuna, Spectral expansion for the singular Dirac system with impulsive conditions, Turk J Math, 42, (2018), 2527 – 2545.
  • [4] D. R. Anderson, G. Sh. Guseinov and J. Hoffacker, Higher-order self-adjoint boundary-value problems on time scales, J. Comput. Appl. Math., 194 (2) (2006) ; 309-342.
  • [5] F. Atici Merdivenci and G. Sh. Guseinov, On Green’s functions and positive solutions for boundary value problems on time scales, J. Comput. Appl. Math., 141 (1-2) (2002); 75-99.
  • [6] M. Bohner and A. Peterson, Dynamic Equations on Time Scales, Birkh¨auser, Boston, 2001.
  • [7] M. Bohner and A. Peterson, (Eds.), Advances in Dynamic Equations on Time Scales, Birkh¨auser, Boston, 2003.
  • [8] T. Gulsen and E. Yilmaz, Spectral theory of Dirac system on time scales, Applicable Analysis, 96(16), (2017), 2684–2694.
  • [9] G. Sh. Guseinov, Self-adjoint boundary value problems on time scales and symmetric Green’s functions, Turkish J. Math., 29 (4); (2005) ; 365􀀀380.
  • [10] G. Sh. Guseinov, Eigenfunction expansions for a Sturm-Liouville problem on time scales. Int. J. Difference Equ. 2 (2007), no. 1, 93–104.
  • [11] G. Sh. Guseinov, An expansion theorem for a Sturm-Liouville operator on semi-unbounded time scales. Adv. Dyn. Syst. Appl. 3 (2008), no. 1, 147–160.
  • [12] S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results Math. 18; (1990); 18􀀀56:
  • [13] G. Hovhannisyan, On Dirac equation on a time scale, Journal of Math. Physics, 52, no.10, 102701, 2011.
  • [14] A. N. Kolmogorov and S. V. Fomin, Introductory Real Analysis. Translated by R.A. Silverman, Dover Publications, New York, 1970.
  • [15] V. Lakshmikantham, S. Sivasundaram and B. Kaymakcalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Dordrecht, 1996.
  • [16] B. M. Levitan and I. S. Sargsjan, Sturm-Liouville and Dirac Operators. Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1991 (translated from the Russian).
  • [17] B. P. Rynne, L2 spaces and boundary value problems on time-scales, J. Math. Anal. Appl. 328; (2007); 1217􀀀1236.
  • [18] B. Thaller, The Dirac Equation, Springer, 1992.
  • [19] E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations. Part I. Second Edition Clarendon Press, Oxford, 1962.
  • [20] J. Weidmann, Spectral Theory of Ordinary Differential Operators, Lecture Notes in Mathematics, 1258, Springer, Berlin 1987.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Bilender P. Allahverdiev Bu kişi benim

Hüseyin Tuna

Yayımlanma Tarihi 15 Nisan 2019
Gönderilme Tarihi 3 Ağustos 2018
Kabul Tarihi 20 Aralık 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 7 Sayı: 1

Kaynak Göster

APA Allahverdiev, B. P., & Tuna, H. (2019). Eigenfunction Expansion in the Singular Case for Dirac Systems on Time Scales. Konuralp Journal of Mathematics, 7(1), 128-135.
AMA Allahverdiev BP, Tuna H. Eigenfunction Expansion in the Singular Case for Dirac Systems on Time Scales. Konuralp J. Math. Nisan 2019;7(1):128-135.
Chicago Allahverdiev, Bilender P., ve Hüseyin Tuna. “Eigenfunction Expansion in the Singular Case for Dirac Systems on Time Scales”. Konuralp Journal of Mathematics 7, sy. 1 (Nisan 2019): 128-35.
EndNote Allahverdiev BP, Tuna H (01 Nisan 2019) Eigenfunction Expansion in the Singular Case for Dirac Systems on Time Scales. Konuralp Journal of Mathematics 7 1 128–135.
IEEE B. P. Allahverdiev ve H. Tuna, “Eigenfunction Expansion in the Singular Case for Dirac Systems on Time Scales”, Konuralp J. Math., c. 7, sy. 1, ss. 128–135, 2019.
ISNAD Allahverdiev, Bilender P. - Tuna, Hüseyin. “Eigenfunction Expansion in the Singular Case for Dirac Systems on Time Scales”. Konuralp Journal of Mathematics 7/1 (Nisan 2019), 128-135.
JAMA Allahverdiev BP, Tuna H. Eigenfunction Expansion in the Singular Case for Dirac Systems on Time Scales. Konuralp J. Math. 2019;7:128–135.
MLA Allahverdiev, Bilender P. ve Hüseyin Tuna. “Eigenfunction Expansion in the Singular Case for Dirac Systems on Time Scales”. Konuralp Journal of Mathematics, c. 7, sy. 1, 2019, ss. 128-35.
Vancouver Allahverdiev BP, Tuna H. Eigenfunction Expansion in the Singular Case for Dirac Systems on Time Scales. Konuralp J. Math. 2019;7(1):128-35.
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