Vol. 54, No. 2, 1974

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Approximation and interpolation for some spaces of analytic functions in the unit disc

Arne Stray

Vol. 54 (1974), No. 2, 237–251

Let U he a bounded open subset of the complex plane C such that U and CU are connected. (If B C,B denotes its closure in C.) H(U) is the space of all bounded analytic functions defined on U. Let S U be She zero set of a nonzero function in H(U). Necessary and sufficient conditions on S are given for the existence of an open sel 0 tU(SS) such that H(0) and H(U) have the same restrictions to S. If U is the unit disc D = {z : |z| < 1} and S is as above, the following result holds for all the Hardy spaces Hp(D), 0 < p ≤∞: Given g Hp(D), there is a function fanalytic in C(SS) such thatf|D Hp(D) andf = g on S.

Mathematical Subject Classification 2000
Primary: 30A78
Secondary: 46J15
Received: 21 November 1972
Published: 1 October 1974
Arne Stray
Mathematics Institute
University of Bergen
5007 Bergen