Dissipative holomorphic functions, Bloch radii, and the Schwarz lemma

DOI10.1007/BF02791228zbMath0972.46029OpenAlexW1964622291WikidataQ124978935 ScholiaQ124978935MaRDI QIDQ5926436

Simeon Reich, Lawrence A. Harris, David M. Shoikhet

Publication date: 2 November 2001

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02791228

zbMATH Keywords

numerical rangeBloch radiidissipative holomorphic functionsLumer-Phillips theoremSchwarz lemma

Mathematics Subject Classification ID

Infinite-dimensional holomorphy (46G20)

Related Items (12)

Growth estimates for the numerical range of holomorphic mappings and applications ⋮ Analytic semigroups of holomorphic mappings and composition operators ⋮ Ergodicity, numerical range, and fixed points of holomorphic mappings ⋮ Random iterations, fixed points and invariant CRF-horospheres in complex Banach spaces ⋮ A Schwarz lemma at the boundary on complex Hilbert balls and applications to starlike mappings ⋮ Loewner chains and nonlinear resolvents of the Carathéodory family on the unit ball in \(\mathbb{C}^n\) ⋮ Asymptotically spirallike mappings in reflexive complex Banach spaces ⋮ A rigidity theorem for holomorphic generators on the Hilbert ball ⋮ Abel averages and holomorphically pseudo-contractive maps in Banach spaces ⋮ A Julia-Carathéodory theorem for hyperbolically monotone mappings in the Hilbert ball ⋮ Abel averages of holomorphic mappings ⋮ A sharpened form of the inverse function theorem

Cites Work

• Dissipative operators in a Banach space
• A nonlinear Hille-Yosida theorem in Banach spaces
• On the size of balls covered by analytic transformations
• Semigroups and generators on convex domains with the hyperbolic metric
• Generation theory for semigroups of holomorphic mappings in Banach spaces
• A continuous form of Schwarz's lemma in normed linear spaces
• Differential Equations on Closed Subsets of a Banach Space
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
• The Numerical Range of Holomorphic Functions in Banach Spaces
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