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Trace Regularization Problem For Higher Order Differential Operator

Yıl 2020, Cilt: 2 Sayı: 1, 27 - 37, 30.04.2020

Öz

We establish a regularized
trace formula for higher order self-adjoint differential operator with
unbounded operator coefficient

Kaynakça

  • [1] E.E. Adıguzelov, About the trace of the difference of two Sturm-Liouville operators with operator coefficient, iz.An Az SSR, seriya fiz-tekn. i mat.nauk, No:5, 20-24, (1976).
  • [2] E.E. Adıguzelov and O. Baksi, On The Regularized Trace of The Differential Operator Equation Given in a Finite Interval, Journal of Engineering and Natural Sciences Sigma, 47-55, 2004/1.
  • [3] N.M. Aslanova, About the spectrum and the trace formula for the operator Bessel equation, Siberian Mathematical Journal, Vol.51, No.4, 569-583, (2010).
  • [4] M. Bayramoglu and E.E. Adıguzelov, On a regularized trace formula for the Sturm-Lioville operator with a bounded operator coefficient and with a singularity, Differential Equations, Vol.32, No.12, 1581-1585, (1996).
  • [5] L.A. Dikiy, About a formula of Gelfand-Levitan, Usp.Mat.Nauk, 82, 119-123, (1953).
  • [6] L.A. Dikiy, The Zeta Function of an ordinary Differential Equation on a finite Interval, IZV. Akad. Nauk.SSSR, Vol.19,4, 187-200, (1955).
  • [7] L.D. Faddeev, On the expression for the trace of the difference of two singular differential operators of the Sturm Liouville Type, Doklady Akademii Nauk SSSR, Vol115, no.5, 878-881, 1957.
  • [8] M.G. Gasymov, On the Sum of Differences of Eigenvalues of Two Self Adjoint Operators, Dokl. Akad. Nauk. SSSR, Vol.150, 6, 1202-1205, (1963).
  • [9] I.M. Gelfand, On The Identities for Eigenvalues of Differential Operator of Second Order, Uspekhi Mat. Nauk (N.S.), 11:1, 191-198, (1956).
  • [10] I.M. Gelfand and B.M. Levitan, On a Formula for Eigenvalues of a Differential Operator of Second Order, Dokl.Akad.Nauk SSSR, T.88, No:4, 593-596, (1953)
  • [11] I.C. Gohberg and M.G. Krein, Introduction to the Theory of Linear Non-self Adjoint Operators, Translation of Mathematical Monographs, Vol.18, AMS, Providence, R.I., (1969).
  • [12] E.E. Adıguzelov, H. Avci, E. G¨ul, The Trace Formula for Sturm-Liouville Operator with Operator Coefficient, J. Math. Phys. 426, 1611-1624, (2001).
  • [13] C.J. Halberg and V.A. Kramer, A generalization of the trace concept, Duke Math.J., 274, 607-618, (1960).
  • [14] R.Z. Halilova, On arranging Sturm-Liouville Operator Equation’s Trace, Funks. Analiz, Teoriya Funksi i ik pril.-Mahachkala, Vol.1, No:3, (1976).
  • [15] D.R. Jafaev, A Trace Formula for the Dirac Operator, Bull, London Math., Soc.37, 908-918, (2005).
  • [16] A.A. Kirillov, Elements of the Theory of Representations, Springer of Verlag, New York, (1976).
  • [17] B.M. Levitan, Calculation of the Regularized Trace for the Sturm Liouville Operator, Uspekhi Mat. Nauk, Vol19,1,161-165, (1964).
  • [18] B.M. Levitan and I.S. Sargsyan, Sturm-Liouville and Dirac Op., Kluwer, Dordrecht, (1991).
  • [19] A.S. Makin, Trace Formulas for the Sturm- Liouville Operator with regular boundary conditions, Dokl. Math., 76, 702-707, (2007).
  • [20] F.G. Maksudov, M. Bayramoglu and E.E. Adıg¨uzelov, On a Regularized Traces of the Sturm-Liouville Operator on a Finite Interval with the Unbounded Operator Coefficient, Dokl.Akad, Nauk SSSR, English translation, Soviet Math, Dokl, 30, No1, 169-173, (1984).
  • [21] V.A. Sadovnichii and V.E. Podolskii, Trace of Differential Operators, Differential Equations, Vol.45, No.4, 477-493, (2009).
  • [22] E. Sen, A. Bayramov and K. Orucoglu, Regularized Trace Formula For Higher Order Differential Operators With Unbounded Coefficients, Electronic Journal of Differential Equations, Vol. 2016 (2016), No. 31, pp. 1-12.
  • [23] C.F. Yang, New Trace Formulae for a Quadratic Pencil of the Schr¨odinger Operator, J. Math. Phys., 51, 033506, (2010).
Yıl 2020, Cilt: 2 Sayı: 1, 27 - 37, 30.04.2020

Öz

Kaynakça

  • [1] E.E. Adıguzelov, About the trace of the difference of two Sturm-Liouville operators with operator coefficient, iz.An Az SSR, seriya fiz-tekn. i mat.nauk, No:5, 20-24, (1976).
  • [2] E.E. Adıguzelov and O. Baksi, On The Regularized Trace of The Differential Operator Equation Given in a Finite Interval, Journal of Engineering and Natural Sciences Sigma, 47-55, 2004/1.
  • [3] N.M. Aslanova, About the spectrum and the trace formula for the operator Bessel equation, Siberian Mathematical Journal, Vol.51, No.4, 569-583, (2010).
  • [4] M. Bayramoglu and E.E. Adıguzelov, On a regularized trace formula for the Sturm-Lioville operator with a bounded operator coefficient and with a singularity, Differential Equations, Vol.32, No.12, 1581-1585, (1996).
  • [5] L.A. Dikiy, About a formula of Gelfand-Levitan, Usp.Mat.Nauk, 82, 119-123, (1953).
  • [6] L.A. Dikiy, The Zeta Function of an ordinary Differential Equation on a finite Interval, IZV. Akad. Nauk.SSSR, Vol.19,4, 187-200, (1955).
  • [7] L.D. Faddeev, On the expression for the trace of the difference of two singular differential operators of the Sturm Liouville Type, Doklady Akademii Nauk SSSR, Vol115, no.5, 878-881, 1957.
  • [8] M.G. Gasymov, On the Sum of Differences of Eigenvalues of Two Self Adjoint Operators, Dokl. Akad. Nauk. SSSR, Vol.150, 6, 1202-1205, (1963).
  • [9] I.M. Gelfand, On The Identities for Eigenvalues of Differential Operator of Second Order, Uspekhi Mat. Nauk (N.S.), 11:1, 191-198, (1956).
  • [10] I.M. Gelfand and B.M. Levitan, On a Formula for Eigenvalues of a Differential Operator of Second Order, Dokl.Akad.Nauk SSSR, T.88, No:4, 593-596, (1953)
  • [11] I.C. Gohberg and M.G. Krein, Introduction to the Theory of Linear Non-self Adjoint Operators, Translation of Mathematical Monographs, Vol.18, AMS, Providence, R.I., (1969).
  • [12] E.E. Adıguzelov, H. Avci, E. G¨ul, The Trace Formula for Sturm-Liouville Operator with Operator Coefficient, J. Math. Phys. 426, 1611-1624, (2001).
  • [13] C.J. Halberg and V.A. Kramer, A generalization of the trace concept, Duke Math.J., 274, 607-618, (1960).
  • [14] R.Z. Halilova, On arranging Sturm-Liouville Operator Equation’s Trace, Funks. Analiz, Teoriya Funksi i ik pril.-Mahachkala, Vol.1, No:3, (1976).
  • [15] D.R. Jafaev, A Trace Formula for the Dirac Operator, Bull, London Math., Soc.37, 908-918, (2005).
  • [16] A.A. Kirillov, Elements of the Theory of Representations, Springer of Verlag, New York, (1976).
  • [17] B.M. Levitan, Calculation of the Regularized Trace for the Sturm Liouville Operator, Uspekhi Mat. Nauk, Vol19,1,161-165, (1964).
  • [18] B.M. Levitan and I.S. Sargsyan, Sturm-Liouville and Dirac Op., Kluwer, Dordrecht, (1991).
  • [19] A.S. Makin, Trace Formulas for the Sturm- Liouville Operator with regular boundary conditions, Dokl. Math., 76, 702-707, (2007).
  • [20] F.G. Maksudov, M. Bayramoglu and E.E. Adıg¨uzelov, On a Regularized Traces of the Sturm-Liouville Operator on a Finite Interval with the Unbounded Operator Coefficient, Dokl.Akad, Nauk SSSR, English translation, Soviet Math, Dokl, 30, No1, 169-173, (1984).
  • [21] V.A. Sadovnichii and V.E. Podolskii, Trace of Differential Operators, Differential Equations, Vol.45, No.4, 477-493, (2009).
  • [22] E. Sen, A. Bayramov and K. Orucoglu, Regularized Trace Formula For Higher Order Differential Operators With Unbounded Coefficients, Electronic Journal of Differential Equations, Vol. 2016 (2016), No. 31, pp. 1-12.
  • [23] C.F. Yang, New Trace Formulae for a Quadratic Pencil of the Schr¨odinger Operator, J. Math. Phys., 51, 033506, (2010).
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Ozlem Bakşi

Yonca Sezer 0000-0003-3072-8302

Serpil Karayel Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2020
Kabul Tarihi 27 Nisan 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 2 Sayı: 1

Kaynak Göster

APA Bakşi, O., Sezer, Y., & Karayel, S. (2020). Trace Regularization Problem For Higher Order Differential Operator. Maltepe Journal of Mathematics, 2(1), 27-37.
AMA Bakşi O, Sezer Y, Karayel S. Trace Regularization Problem For Higher Order Differential Operator. Maltepe Journal of Mathematics. Nisan 2020;2(1):27-37.
Chicago Bakşi, Ozlem, Yonca Sezer, ve Serpil Karayel. “Trace Regularization Problem For Higher Order Differential Operator”. Maltepe Journal of Mathematics 2, sy. 1 (Nisan 2020): 27-37.
EndNote Bakşi O, Sezer Y, Karayel S (01 Nisan 2020) Trace Regularization Problem For Higher Order Differential Operator. Maltepe Journal of Mathematics 2 1 27–37.
IEEE O. Bakşi, Y. Sezer, ve S. Karayel, “Trace Regularization Problem For Higher Order Differential Operator”, Maltepe Journal of Mathematics, c. 2, sy. 1, ss. 27–37, 2020.
ISNAD Bakşi, Ozlem vd. “Trace Regularization Problem For Higher Order Differential Operator”. Maltepe Journal of Mathematics 2/1 (Nisan 2020), 27-37.
JAMA Bakşi O, Sezer Y, Karayel S. Trace Regularization Problem For Higher Order Differential Operator. Maltepe Journal of Mathematics. 2020;2:27–37.
MLA Bakşi, Ozlem vd. “Trace Regularization Problem For Higher Order Differential Operator”. Maltepe Journal of Mathematics, c. 2, sy. 1, 2020, ss. 27-37.
Vancouver Bakşi O, Sezer Y, Karayel S. Trace Regularization Problem For Higher Order Differential Operator. Maltepe Journal of Mathematics. 2020;2(1):27-3.

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