Abstract
A closed subset E of the unit circumference T is said to be a peak set for the analytic Holder class Aα, 0 < α < 1 there exists a functionf,f∈Aα such that f¦E≡1 and ¦f(z)¦<1 for . It is shown that the set E is a peak set of the algebra Aα if and only if there exists a nonnegative Borel measure μ on T such that the function coincides almost everywhere with a function of the Holder class ⋀α, equal to zero on E. A sufficient condition in order that a closed set E should belong to the family of peak sets is obtained.
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