Analyticity of semigroups on the right half-plane

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• 作者：Mark Elin ^{mark_elin@braude.ac.il} ; Fiana Jacobzon ; ^{fiana@braude.ac.il}
• 关键词：Holomorphic mapping ; Semigroup ; Composition operator ; Hardy space ; Function convex in one direction
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：750-766
• 全文大小：433 K
• 卷排序：448

文摘

This paper is devoted to the study of semigroups of composition operators and semigroups of holomorphic mappings. We establish conditions under which these semigroups can be extended in their parameter to a sector given a priori. We show that the size of this sector can be controlled by the image properties of the infinitesimal generator, or, equivalently, by the geometry of the so-called associated planar domain. We also give a complete characterization of all composition operators acting on the Hardy space HpHp on the right half-plane.