ARBITRARY-ORDER ASYMPTOTICS FOR THE EIGENVALUES OF THE ORDINARY DIFFERENTIAL OPERATORS WITH SUMMABLE COEFFICIENTS

Yıl 2006, Cilt: 8 Sayı: 2, 111 - 119, 01.05.2006

Alp Arslan Kıraç

Öz

In this article, we obtain the asymptotic formulas of arbitrary order for the eigenvalues of
the differential operator generated by ordinary differential equation with summable
coefficients and t -periodic boundary conditions

Anahtar Kelimeler

Non-self-adjoint differential operators, t -periodic boundary conditions, Asymptotic formulas

TOPLANABİLEN KATSAYILI ADİ DİFERANSİYEL OPERATÖRLERİN ÖZDEĞERLERİ İÇİN KEYFİ MERTEBE ASİMPTOTİKLER

Öz

Bu makalede, toplanabilen katsayılara sahip adi diferansiyel denklem ve t -periyodik sınır
koşulları tarafından üretilen diferansiyel operatörün özdeğerleri için keyfi mertebeden
asimptotik formüller elde edild

Anahtar Kelimeler

Self-adjoint olmayan diferansiyel operatörler, t -periyodik sınır koşulları, Asimptotik formüller

Kaynakça

• Birkhoff G.D. (1908): “Boundary Value and Expansion Problems of Ordinary Linear Differential Equations”, Trans. Amer. Math. Soc., 9, pp. 373-95.
• Eastham M.S.P. (1973): “The Spectral Theory of Periodic Differential Equations”, Scottish Acedemic Pres, Edinburg.
• Naimark M.A. (1967): “Linear Differential Operators”, Volume I, George G. Harap and Company Ltd., London.
• Tamarkin J.D. (1927): “Some General Problems of The Theory of Ordinary Linear Differential Equations and Expansion of an Arbitrary Function in Series of Fundamental Functions”, Math. Zeit., 27, pp. 1-54.
• Veliev O.A. (1983): “The Spectrum and Spectral Singularities of Differential Operators with Complex-Valued Periodic Coefficients”, Differential Cprime nye Uravneniya, 19, pp. 1316-1324.
• Veliev O.A. (1986): “Spectral Expansion Related to Non-Selfadjoint Diffrential Operator with Periodic Coefficients” (Russian, English), Diffrential Equations, 22 (12), pp. 1403- 1408.
• Veliev O.A., Duman M.T. (2002): “The Spectral Expansion for a Nonself-Adjoint Hill Operator with a Locally Integrable Potential”, J. Math. Anal. Appl., 265, pp. 76-90.