OPTIMAL SAMPLING OF PERIODIC ANALYTIC-FUNCTIONS

Let S = (z ∈ C : |Im(z)| < β) be a strip in the complex plane. H˜2 denotes the space of functions f, which are analytic and 2π-periodic in S and satisfy [GRAPHICS] The Kolmogorov n-widths dn, Gel′fand n-widths dn, and linear n-widths δn of H˜2 in L˜2, the periodic Lebesgue space on the real axis are determined by [GRAPHICS] The same equations hold for dn(H˜2, L˜2) and δn(H˜2, L˜2). Fourier expansion of order 2n - 1 is an optimal linear approximation operator for δ2n - 1 = δ2n. In addition, we construct an optimal linear 2n-dimensional approximarion method, which is based in sampling a function f ∈ H˜2 in 2n equidistant points in [0, 2π]. © 1995 Academic Press, Inc.