Journal of the
Korean Mathematical Society JKMS

The spectral problem \[\begin{matrix} -{y}''+q(x)y=\lambda y,{ }00,{{c}_{1}}<{{c}_{2}}<\cdots<{{c}_{N}},N\ge 0.$ The sharpened asymptotic formulae for eigenvalues and eigenfunctions of above-mentioned spectral problem are obtained and the uniform convergence of the spectral expansions of the continuous functions in terms of eigenfunctions are presented.

Keywords: differential operator, eigenvalues, uniform convergence of spectral expansion

MSC numbers: 34B05, 34B24, 34L10, 34L20