Does every contractive analytic function in a polydisk have a dissipative n-dimensional scattering realization?
Functional Analysis
2012-01-17 v1 Complex Variables
Abstract
No. The title question was posed by D. Kalyuzhnyi-Verbovetskyi [1, Problem 1.3]. Let \mathcal{L(H,K)} denote the set of all bounded linear operators between a pair of Hilbert spaces \mathcal{H,K}, and let \mathbb{D}^{n} and \mathbb{T}^{n} denote the open unit polydisk, and the unit n-torus, respectively.
Cite
@article{arxiv.1201.3286,
title = {Does every contractive analytic function in a polydisk have a dissipative n-dimensional scattering realization?},
author = {Michael T. Jury},
journal= {arXiv preprint arXiv:1201.3286},
year = {2012}
}
Comments
4 pages