On the Sundberg approximation theorem

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• 作者：Alexander Brudnyi¹ ; ^{albru@math.ucalgary.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 30E10 ; secondary ; 30J99
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：19 March 2016
• 年：2016
• 卷：291
• 期：Complete
• 页码：774-783
• 全文大小：315 K

文摘

Let H^∞$H^{\infty }$ be the Banach algebra of bounded holomorphic functions on the open unit disk D⊂C$\mathbb{D}\subset \mathbb{C}$. We extend Sundberg's theorem on uniform approximation of functions in BMOA   by H^∞$H^{\infty }$ functions to other classes of holomorphic functions on D$\mathbb{D}$. In our proofs we use a new characterization of meromorphic functions on D$\mathbb{D}$ that extend to continuous maps of the maximal ideal space of H^∞$H^{\infty }$ to the Riemann sphere.