Operator theory and the Oka extension theorem

Jim Agler; John E. McCarthy

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arXiv · 1212.5282

Operator theory and the Oka extension theorem

Jim Agler·John E. McCarthy

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Abstract

For $\delta$ an $m$-tuple of analytic functions, we define an algebra $\hidg$, contained in the bounded analytic functions on the analytic polyhedron $ {|\delta^l(z)| < 1, \ 1 \leq l \leq m}$, and prove a representation formula for it. We give conditions whereby every function that is analytic on a neighborhood of $ {|\delta^l(z)| \leq 1, \ 1 \leq l \leq m}$ is actually in $\hidg$. We use this to give a proof of the Oka extension theorem with bounds. We define an $\hidg$ functional calculus for operators.

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Jim Agler, John E. McCarthy. 2012-12-20. Operator theory and the Oka extension theorem. https://arxiv.org/abs/1212.5282

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