Regularity of a Problem of 3n-th Order with Decaying Boundary-Value Conditions

Abstract

Let us consider on interval (0, 1) a differential pencil with three n-fold characteristic roots and decaying boundary-value conditions, only one of which is related to the end of 1. We solve problem of expanding of 3n times continuously differentiable function into a Fourier series in the root elements of the pencil. The studied problem essentially generalizes the previous considerations, which concern only the relatively simple cases of pencils with two n-fold characteristic roots. New method are used in estimating the resolvent of the problem. As for the problem under consideration with three n-fold characteristics, it dose not fit into the solution scheme of previous works and is associated with overcoming of exact constructions and calculations.