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V Peller, S Khrushchev (1982)
Hankel operators, best approximations, and stationary Gaussian processesRussian Mathematical Surveys, 37
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ON BEST UNIFORM APPROXIMATION BY BOUNDED ANALYTIC FUNCTIONS M. PAPADIMITRAKIS C{T) is the space of continuous functions on the unit circle 7 with the supremum 0O norm || • || i/ (r) is the space of nontangential limits of bounded analytic functions 0O X 1 in the unit disc D. Also, A(T) = H (T) n C(T). Let Ft be the subspace of C(T) of all functions whose Fourier series is absolutely convergent with norm ll/ll ^ = EL/t»)l, An) = H\T)\s the Hardy space of nontangential limits of functions F analytic in D such that \\F\\ = sup f|F(r^|^<+cx), 0 < r < 1 J *- and H\(T) = {FeH\T)\ F(0) = 0}. It is known (see [2]) that any/ e C(T) has a unique best approximation geH°°(r) in the sense d=d(f,H™)= inf H/-AIL = ||/-^L , and that, by duality, There is also (at least) one F for which the sup (*) is attained. / , g and any of those maximizing F are connected by We agree to write g = T(J). Generally, differentiability properties of/ar e preserved by g; see [1,2]. 1 1 It is also known (see [3] for more information) that/e^Y implies ge^Y
Bulletin of the London Mathematical Society – Wiley
Published: Jan 1, 1996
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