Interpolation avec contraintes sur des ensembles finis du disque

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• 作者：Rachid Zarouf
• 刊名：Comptes Rendus Mathematique
• 出版年：2009
• 出版时间：July 2009
• 年：2009
• 卷：347
• 期：13-14
• 页码：785-790
• 全文大小：147 K

文摘

Given a finite set σ of the unit disc and a holomorphic function f in which belongs to a class X, we are looking for a function g in another class Y (smaller than X) which minimizes the norm g_Y among all functions g such that g_σ=f_σ. For Y=H^∞, and for the corresponding interpolation constant c(σ,X,H^∞), we show that where n=#σ, r=max_λσλ and where φ_X(t) stands for the norm of the evaluation functional ff(λ) on the space X. The upper bound is sharp over sets σ with given n and r. To cite this article: R. Zarouf, C. R. Acad. Sci. Paris, Ser. I 347 (2009).