IJPAM: Volume 26, No. 2 (2006)

ON THE SPECTRUM OF THE BUNDLE OF SECOND
ORDER DIFFERENTIAL OPERATORS WITH ALMOST
PERIODIC COEFFICIENTS

A.D. Orujov
Department of Mathematics
Faculty of Science and Art
Cumhuriyet University
Sivas, 58140, TURKEY
e-mail: eorucov@cumhuriyet.edu.tr


Abstract.In this paper, spectrum and resolvent of operator $L_{\lambda }$ which is generated by differential expression $\ell _{\lambda }(y)=-y^{\prime \prime }+(p_{1}\lambda
+q_{1}(x))y^{\prime }+(p_{2}\lambda ^{2}+\lambda q_{2}(x)+q_{3}(x))y$ have been investigated in the space $L_{2}(R)$. Here the coefficients $q_{j}(x),q_{1}^{\prime }(x)$ are Bohr almost periodic functions whose fourier series are absolutely convergent. Fourier exponents of coefficients are positive and only have limit point at $+\infty $. It has been shown that spectrum of operator is pure continous and it consists of two lines (they can also coincide) which pass from the origin. Moreover simple spectral singularities can exist over the continous spectrum.

Received: October 28, 2005

AMS Subject Classification: 34L05, 47E05

Key Words and Phrases: almost periodic, spectrum, resolvent, spectral singularity

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 2