Divergence of trigonometric lacunary interpolation

On the divergence of trigonometric lacunary interpolation

“…Furthermore, P. Nevai and P. V~rtesi[4] succeeded in establishing a divergence result not only in a single point, but also on a set of full measure: Let wM(t) satisfy (1-3), and let (en) be a sequence of positive numbers such that limn--.co nMwM(1/n)s 2 = co, limn--.,o sin = co, and limn--,oo sn = 0. Then there exists a function f E C2~(WM) such that nmsup IR~(f;x)-f(x)the aim of this note to show that the sequence (En) is indeed dispensable.…”