Asymptotic Expansion for the Lebesgue Constants of the Walsh System
نویسنده
چکیده
Let Lk denote the Lebesgue constants of the Walsh system. The following exact result is established by means of Mellin transforms: ∑ 1≤k<n Lk = n 4 log2 n+ nF (log2 n)− Ln 2 , for n ≥ 1, where F (u) is a continuous periodic function with period 1 whose Fourier coefficients can be explicitly expressed in terms of Riemann’s zeta function. This improves an old result of Fine.
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تاریخ انتشار 1995