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Trace Regularization Problem For Higher Order Differential Operator

Year 2020, Volume: 2 Issue: 1, 27 - 37, 30.04.2020

Abstract

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

References

  • [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).
Year 2020, Volume: 2 Issue: 1, 27 - 37, 30.04.2020

Abstract

References

  • [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).
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ozlem Bakşi

Yonca Sezer 0000-0003-3072-8302

Serpil Karayel This is me

Publication Date April 30, 2020
Acceptance Date April 27, 2020
Published in Issue Year 2020 Volume: 2 Issue: 1

Cite

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. April 2020;2(1):27-37.
Chicago Bakşi, Ozlem, Yonca Sezer, and Serpil Karayel. “Trace Regularization Problem For Higher Order Differential Operator”. Maltepe Journal of Mathematics 2, no. 1 (April 2020): 27-37.
EndNote Bakşi O, Sezer Y, Karayel S (April 1, 2020) Trace Regularization Problem For Higher Order Differential Operator. Maltepe Journal of Mathematics 2 1 27–37.
IEEE O. Bakşi, Y. Sezer, and S. Karayel, “Trace Regularization Problem For Higher Order Differential Operator”, Maltepe Journal of Mathematics, vol. 2, no. 1, pp. 27–37, 2020.
ISNAD Bakşi, Ozlem et al. “Trace Regularization Problem For Higher Order Differential Operator”. Maltepe Journal of Mathematics 2/1 (April 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 et al. “Trace Regularization Problem For Higher Order Differential Operator”. Maltepe Journal of Mathematics, vol. 2, no. 1, 2020, pp. 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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