The asymptotic distribution of zeros of minimal Blaschke products. (English) Zbl 0923.30022
Let \(B\) be a Blaschke product of degree \(n\geq 1\) and \(B_n\) the set of all Blaschke products of degree \(n\) or less. Let \(W\) be a nonnegative continuous function on the open unit disc \(D\) and \(E\) a compact subset of \(D\). The authors study the asymptotic distribution, as \(n\to\infty\), of the zeros of the solutions to the extremal problem: \(\min\{\| BW^n\|_E;\;B\in B_n\}\) where \(\|\cdot \|_E\) is the sup norm over \(E\). They study it beyond Blaschke products and the unit disc.
Reviewer: T.Nakazi (Sapporo)
MSC:
| 30D50 | Blaschke products, etc. (MSC2000) |
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