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arXiv · 1201.3286

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

Michael T. Jury
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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.

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Michael T. Jury. 2012-01-16. Does every contractive analytic function in a polydisk have a dissipative n-dimensional scattering realization?. https://arxiv.org/abs/1201.3286

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