The present review contains results of V. A. Il’in and his pupils concerning an assessment of speed of convergence and equiconvergence with a trigonometrical series of Fourier of spectral decomposition of functions on root functions of linear ordinary differential operators both self-conjugate, and not self-conjugate, set on a final piece of a numerical straight line. The first theorem of V. A. Ilyin of equiconvergence of spectral decomposition for the differential operator of any order is provided.
