On the arclength of trigonometric interpolants

On the arclength of trigonometric interpolants

Blog Article

As pointed out recently by Strichartz [5], the arclength of the graph (Gamma(S_N(f))) of the partial sums (S_N(f)) of the Fourier series of a jump function (f) grows with the order of (log walter hagenah me 262 N).In this paper we discuss the behaviour of the arclengths of the graphs of trigonometric interpolants orly impressions to a jump function.Here the boundedness of the arclengths depends essentially on the fact whether the jump discontinuity is at an interpolation point or not.In addition convergence results for the arclengths of interpolants to smoother functions are presented.