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arXiv · 1912.09186

K-inner functions and K-contractions

Jörg Eschmeier·Sebastian Toth
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Abstract

For a large class of unitarily invariant reproducing kernel functions $K$ on the unit ball $\mathbb B_d$ in $\mathbb C^d$, we characterize the $K$-inner functions on $\mathbb B_d$ as functions admitting a suitable transfer function realization. We associate with each $K$-contraction $T \in L(H)^d$ a canonical operator-valued $K$-inner function and extend a uniqueness theorem of Arveson for minimal $K$-dilations to our setting. We thus generalize results of Olofsson for $m$-hypercontractions on the unit disc and of the first named author for $m$-hypercontractions on the unit ball.

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Jörg Eschmeier, Sebastian Toth. 2019-12-19. K-inner functions and K-contractions. https://arxiv.org/abs/1912.09186

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