Nevanlinna representations in several variables
Complex Variables
2012-06-26 v2
Abstract
We generalize two integral representation formulae of Nevanlinna to functions of several variables. We show that for a large class of analytic functions that have non-negative imaginary part on the upper polyhalfplane there are representation formulae in terms of densely defined self-adjoint operators on a Hilbert space. We introduce three types of structured resolvent of a self-adjoint operator and identify four different types of representation in terms of these resolvents. We relate the types of representation that a function admits to its growth at infinity.
Keywords
Cite
@article{arxiv.1203.2261,
title = {Nevanlinna representations in several variables},
author = {Jim Agler and R. Tully-Doyle and N. J. Young},
journal= {arXiv preprint arXiv:1203.2261},
year = {2012}
}
Comments
37 pages. In this version we have added some references and expanded the introduction