Research Article

The Regularized Trace Formula Of A Second Order Differentıal Equation Given With Anti-Perıodic Boundary Conditions

Volume: 40 Number: 4 December 31, 2019
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The Regularized Trace Formula Of A Second Order Differentıal Equation Given With Anti-Perıodic Boundary Conditions

Abstract

In this study, we examined the formula of the regularized trace of the self-adjoint operator which is formed by

differential expression and

 

anti-periodic boundary condition.

Keywords

References

  1. [1] Gelfand, I. M. and Levitan, B. M., On a formula for eigenvalues of a differential operator of second order. Dokl. Akad. Nauk SSSR, 88-4 (1953) 593-596.
  2. [2] Dikii, L. A., On a Formula of Gelfand–Levitan. Usp. Mat. Nauk, 8-2 (1953) 119-123.
  3. [3] Gelfand, I. M., About an identity for eigenvalues of a differential operator of second order. Usp. Mat. Nauk, 11(67) (1956) 191-198.
  4. [4] Fadeev, L.D., On the Expression for the Trace of the Difference of Two Singular Differential Operators of the Sturm–Liouville Type. Dokl. Akad. Nauk SSSR, 115-5 (1957) 878– 881.
  5. [5] Dikii, L. A., Trace formulas for differential operators of Sturm- Liouville. Uspeki Matem. Nauk, 13-3 (1958) 111-143.
  6. [6] Levitan, B.M., Calculation of the Regularized Trace for the Sturm–Liouville Operator. Uspekhi Mat. Nauk, 19-1 (1964) 161–165.
  7. [7] Sadovnichii,V.A.,On the trace of the difference of two high-order ordinary differential operators. Differents, Uravneniya, 2-12 (1966) 1611-1624.
  8. [8] Cao, C.W. and Zhuang, D.W., Some trace formulas for the Schr¨odinger equation with energy-dependent potential, Acta Math. Sci.(in Chinese), 5 (1985) 233-236.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Leyla Özen
Türkiye

Publication Date

December 31, 2019

Submission Date

November 9, 2018

Acceptance Date

October 24, 2019

Published in Issue

Year 2019 Volume: 40 Number: 4

APA
Kızılbudak Çalışkan, S., & Özen, L. (2019). The Regularized Trace Formula Of A Second Order Differentıal Equation Given With Anti-Perıodic Boundary Conditions. Cumhuriyet Science Journal, 40(4), 784-791. https://doi.org/10.17776/csj.480810

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