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Interpolating sequences in mean. (English) Zbl 1417.30027

The author considers interpolation problems in the space of bounded analytic functions in the disk as well as in spaces of analytic Hölder functions. Given a target sequence \(\{w_n\}_{n\ge1}\) and a sequence of points \(\{z_n\}_{n\ge1}\) in the unit disc, the author searches for functions \(f\) in the given class that satisfy the equalities \[ \frac{f(z_1)+\cdots+f(z_n)}{n}=w_n,\quad n\ge1. \] He describes target spaces when the corresponding interpolating sequences are uniformly separated or the union of two uniformly separated sequences.

MSC:

30E05 Moment problems and interpolation problems in the complex plane
30H05 Spaces of bounded analytic functions of one complex variable
30H10 Hardy spaces
26A16 Lipschitz (Hölder) classes
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References:

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