Ergodicity, numerical range, and fixed points of holomorphic mappings

被引：0
|
作者：
Simeon Reich
David Shoikhet
Jaroslav Zemánek
机构：
[1] The Technion — Israel Institute of Technology,Department of Mathematics
[2] Ort Braude College,Department of Mathematics
[3] Polish Academy of Sciences,Institute of Mathematics
来源：
Journal d'Analyse Mathématique | 2013年 / 119卷
关键词：
Holomorphic Mapping; Nonexpansive Mapping; Numerical Range; Complex Banach Space; Volterra Operator;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we study the local structure of the fixed point set of a holomorphic mapping defined on a (not necessarily bounded or convex) domain in a complex Banach space, using ergodic theory of linear operators and the nonlinear numerical range introduced by L. A. Harris. We provide several constructions of holomorphic retractions and a generalization of Cartan’s Uniqueness Theorem. We also estimate the deviation of a holomorphic mapping from its linear approximation, the Fréchet derivative at a fixed point.
引用
收藏
页码：275 / 303
页数：28
相关论文
共 50 条
  • [11] CONVEXITY OF CARATHEODORY DISTANCE AND FIXED-POINTS OF HOLOMORPHIC MAPPINGS
    MAZET, P
    VIGUE, JP
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 1992, 116 (03): : 285 - 305
  • [12] Common fixed points of holomorphic mappings and retracts of B∞H
    Budzynska, M
    Kuczumow, T
    [J]. COMPLEX ANALYSIS AND DYNAMICAL SYSTEMS: ISRAEL MATHEMATICAL CONFERENCE PROCEEDINGS, 2004, 364 : 35 - 40
  • [13] Holomorphic mappings of the unit disc into itself with two fixed points
    Goryainov, V. V.
    [J]. SBORNIK MATHEMATICS, 2017, 208 (03) : 360 - 376
  • [14] Fixed points for mappings with the range type condition
    García-Falset, J
    [J]. HOUSTON JOURNAL OF MATHEMATICS, 2002, 28 (01): : 143 - 158
  • [15] Growth Estimates for the Numerical Range of Holomorphic Mappings and Applications
    Filippo Bracci
    Marina Levenshtein
    Simeon Reich
    David Shoikhet
    [J]. Computational Methods and Function Theory, 2016, 16 : 457 - 487
  • [16] Growth Estimates for the Numerical Range of Holomorphic Mappings and Applications
    Bracci, Filippo
    Levenshtein, Marina
    Reich, Simeon
    Shoikhet, David
    [J]. COMPUTATIONAL METHODS AND FUNCTION THEORY, 2016, 16 (03) : 457 - 487
  • [17] Fixed points of holomorphic mappings and semigroups in Banach spaces: Regularity and uniqueness
    Khatskevich, V
    Reich, S
    Shoikhet, D
    [J]. INTERACTION BETWEEN FUNCTIONAL ANALYSIS, HARMONIC ANALYSIS, AND PROBABILITY, 1996, 175 : 249 - 254
  • [18] Fixed points of commuting holomorphic mappings other than the Wolff point
    Bracci, F
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 355 (06) : 2569 - 2584
  • [19] FIXED-POINTS AND INVARIANT DOMAINS OF HOLOMORPHIC MAPPINGS OF THE HILBERT BALL
    GOEBEL, K
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1982, 6 (12) : 1327 - 1334
  • [20] Estimate of the Second Coefficient of Holomorphic Mappings of a Disk into Itself with Two Fixed Points
    Kudryavtseva, O. S.
    Solodov, A. P.
    [J]. MATHEMATICAL NOTES, 2023, 113 (5-6) : 694 - 699
12345