Optimal Approximation of Periodic Analytic Functions with Integrable Boundary Values

AbstractLetS=[z∈C: |Im(z)|<β] be a strip in the complex plane.Hq, 1⩽q<∞, denotes the space of functions, which are analytic and 2π-periodic inS, real-valued on the real axis, and possessq-integrable boundary values. Letμbe a positive measure on [0, 2π] andLp(μ) be the corresponding Lebesgue space of periodic real-valued functions on the real axis. The even dimensional Kolmogorov, Gel'fand, and linear widths of the unit ball ofHqinLp(μ) are determined exactly, when 1⩽p⩽q<∞ or when=q<p<∞ andβis sufficiently large. It is shown that all threen-widths coincide and a characterization of the widths in terms of Blaschke products is established