A uniqueness theorem for bounded analytic functions on the polydisc

Details A uniqueness theorem for bounded analytic functions on the polydisc A uniqueness theorem for bounded analytic functions on the polydisc

2010-12-15

arxiv.org/abs/1012.3412v2

Mathematics

Complex Variables

7 pages, corrected typo in Abstract

Scientific paper

For each n,N>0 we construct a set of points x_1,...,x_M in D^n with the following property: if f is a rational inner function on D^n of degree strictly less than N and g is an analytic function mapping D^n to D that satisfies g(x_i)=f(x_i) for each i=1,...,M, then g=f on D^n. In terms of the Pick problem on D^n, our result implies that for any rational inner f of degree less than N, the Pick problem with data x_1,...,x_M and f(x_1),...,f(x_M) has a unique solution.

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