Does every contractive analytic function in a polydisk have a dissipative n-dimensional scattering realization?

Mathematics – Functional Analysis

Scientific paper

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Scientific paper

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.

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