On bounded analytic functions in finitely connected domains

Slodkowski, Zbigniew

doi:10.1090/S0002-9947-1987-0876475-9

On bounded analytic functions in finitely connected domains
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Trans. Amer. Math. Soc. 300 (1987), 721-736 Request permission

Abstract:

A new proof of the corona theorem for finitely connected domains is given. It is based on a result on the existence of a meromorphic selection from an analytic set-valued function. The latter fact is also applied to the study of finitely generated ideals of ${H^\infty }$ over multiply connected domains.

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