On the arclength of trigonometric interpolants

On the arclength of trigonometric interpolants

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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 5x4 tattoo (log N).In this paper we discuss the behaviour of the arclengths of the graphs of trigonometric interpolants to a jump function.Here the boundedness of the arclengths depends essentially mvs10 scooter 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.