Ters periyodik sınır koşulları ile verilmiş ikinci mertebeden diferansiyel denklemin düzenli iz formülü

Yıl 2019, Cilt: 40 Sayı: 4, 784 - 791, 31.12.2019

Seda Kızılbudak Çalışkan Leyla Özen

https://doi.org/10.17776/csj.480810

Öz

Bu çalışmada,

l(y)= -y''+p(x)y

diferansiyel ifadesi ve

y(0)+y(pi)=0

y'(0)+y'(pi)=0

ters sınır koşulları ile oluşturulan kendine eş operatörün düzenli iz formülü incelenmiştir.

Anahtar Kelimeler

düzenli iz, özdeğer, özfonksiyon

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

Öz

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.

Anahtar Kelimeler

regularized trace, eigenvalues, eigenfunctions

Kaynakça

• [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] Dikii, L. A., On a Formula of Gelfand–Levitan. Usp. Mat. Nauk, 8-2 (1953) 119-123.
• [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] 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] Dikii, L. A., Trace formulas for differential operators of Sturm- Liouville. Uspeki Matem. Nauk, 13-3 (1958) 111-143.
• [6] Levitan, B.M., Calculation of the Regularized Trace for the Sturm–Liouville Operator. Uspekhi Mat. Nauk, 19-1 (1964) 161–165.
• [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] 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.
• [9] Bayramoğlu, M., On the regularized trace formula of th differential equation with unbounded Coefficient. Spectral Theory and Its Applications, 7 (1987) 15-40.
• [10] Lax P. D., Trace formulas for the Schroeding operator. Commun. Pure Appl. Math., 47- 4 (1994) 503-512.
• [11] Papanicolaou, V.G., Trace formulas and the behavior of large eigenvalues, SIAM J. Math. Anal., 26 (1995), 218-237.
• [12] Adıgüzelov, E. E., Baykal, O. and Bayramov, A., On the spectrum and regularized trace of the Sturm-Liouville problem with spectral parameter on the boundary condition and with the operator coefficient. International Journal of Differential Equations and Applications, 2-3 (2001) 317-333.
• [13] Savchuk, A.M., Shkalikov, A.A., Trace formula for Sturm-Liouville Operators with Singular Potentials. Mathematical Notes, 69-3 (2001).
• [14] Bayramov, A., Öztürk Uslu, S. and Kızılbudak Çalışkan, S., On the trace formula of second order differential equation given with non-seperable boundary conditions. Sigma Journal of Engineering and Natural Sciences, 4 (2005) 57-64.
• [15] Guliyev, N.J., The regularized trace formula for the Sturm-Liouville equation with spectral parameter in the boundary condition. Proceedins of IMM of NAS of Azerbaijan, 22 (2005) 99-102.
• [16] Sadovnichii, V.A. and Podol’skii, V.E., Traces of Differential Operators. Differential Equations, 45- 4 (2009) 477-493
• [17] Wang, Y.P., Koyunbakan H. and Yang, C.F., A Trace Formula for Integro-differential Operators on the Finite Interval, Acta Mathematicae Applicatae Sinica (English Series) 33-1 (2017) 141-146.