A uniqueness theorem for bounded analytic functions on the polydisc
Complex Variables
2010-12-17 v2
Abstract
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.
Cite
@article{arxiv.1012.3412,
title = {A uniqueness theorem for bounded analytic functions on the polydisc},
author = {David Scheinker},
journal= {arXiv preprint arXiv:1012.3412},
year = {2010}
}
Comments
7 pages, corrected typo in Abstract