Convergence of the Spectral Expansion in the Eigenfunctions of a Fourth-Order Differential Operator

Аннотация

We study the convergence of spectral expansions of functions of the class W_p¹ (G), p ≥ 1, G = (0, 1), in the eigenfunctions of an ordinary differential operator of even order with integrable coefficients. Sufficient conditions for absolute and uniform convergence are obtained and the rate of uniform convergence of these expansions on the interval ̅G is found.