Electron. J. Diff. Equ., Vol. 2016 (2016), No. 80, pp. 1-14.

Uniform convergence of the spectral expansions in terms of root functions for a spectral problem

Nazim B. Kerimov, Sertac Goktas, Emir A. Maris

Abstract:
In this article, we consider the spectral problem
$$\displaylines{ -y''+q(x)y=\lambda y,\quad 0<x<1,\cr y'(0)\sin \beta =y(0)\cos \beta , \quad 0\le \beta <\pi ; \quad y'(1)=(a\lambda +b)y(1) }$$
where $\lambda $ is a spectral parameter, a and b are real constants and a<0, q(x) is a real-valued continuous function on the interval [0,1]. The root function system of this problem can also consist of associated functions. We investigate the uniform convergence of the spectral expansions in terms of root functions.

Submitted February 22, 2016. Published March 18, 2016.
Math Subject Classifications: 34B05, 34B24, 34L10, 34L20.
Key Words: Differential Operator; eigenvalues; root functions; uniform convergence of spectral expansion.

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Nazim B. Kerimov
Department of Mathematics
Mersin University
33343, Mersin, Turkey
email: nazimkerimov@yahoo.com
Sertac Goktas
Department of Mathematics
Mersin University
33343, Mersin, Turkey
email: srtcgoktas@gmail.com
Emir A. Maris
Department of Mathematics
Mersin University
33343, Mersin, Turkey
email: ealimaris@gmail.com

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