Regularity of a problem of $3n$-th order with decaying boundary-value conditions

On the interval $(0, 1)$ we consider a differential beam with three $n$-fold characteristic roots and decaying boundary conditions, only one of which is assigned to the end $1$. The problem of decomposition of a $3n$-fold continuously differentiable function into a Fourier series by the root elements of the beam is solved. The studied problem essentially generalizes the previous considerations which concerned only relatively simple cases of sheaves with one and two $n$-fold characteristic roots. New methods are used in estimating the resolvent of the problem.