Approximation of discontinuous functions in the Hausdorff metric (Q1076266)

The author denotes: c(f)\(=^{df}\underline{\lim}_{n\to \infty}nHE_ n(f)\) where \(HE_ n(f)\) is the smallest distance in the sense of Hausdorff metric between the function f and the trigonometric polynomials of order \(\leq n\). The aim of the present paper is to give some evaluations of the behaviour of the function f near the discontinuity points in the case c(f)\(\geq \pi /2\). (It is known that if \(c(f)<\pi /2\), then f is continuous everywhere.)