Matrix-Valued Corona Theorem for Multiply Connected Domains

Details Matrix-Valued Corona Theorem for Multiply Connected Domains Matrix-Valued Corona Theorem for Multiply Connected Domains

1999-02-05

arxiv.org/abs/math/9902046v1

Mathematics

Complex Variables

6 pages

Scientific paper

Let $D\subset\Co$ be a bounded domain, whose boundary $B$ consists of $k$
simple closed continuous curves and $H^{\infty}(D)$ be the algebra of bounded
analytic functions on $D$. We prove the matrix-valued corona theorem for
matrices with entries in $H^{\infty}(D)$.

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