The Takagi problem on the disk and bidisk
Functional Analysis
2012-08-15 v1 Complex Variables
Abstract
We give a new proof on the disk that a Pick problem can be solved by a rational function that is unimodular on the unit circle and for which the number of poles inside the disk is no more than the number of non-positive eigenvalues of the Pick matrix. We use this method to find rational solutions to Pick problems on the bidisk.
Cite
@article{arxiv.1208.2704,
title = {The Takagi problem on the disk and bidisk},
author = {Jim Agler and Joseph A. Ball and John E. McCarthy},
journal= {arXiv preprint arXiv:1208.2704},
year = {2012}
}