The Gibbs phenomenon for general Franklin systems

详细

The paper is devoted to the Gibbs phenomenon for series by general Franklin systems. The general Franklin system corresponding to a given dense sequence of points T = (t_n, n ≥ 0) in [0, 1] is a sequence of orthonormal piecewise linear functions with knots from T, that is, the nth function from the system has knots t₀,..., t_n. The main result of this paper is that the Gibbs phenomenon for Fourier series by general Franklin systems occurs for almost all points of [0, 1].