Journal d’Analyse Mathématique

, Volume 82, Issue 1, pp 221–232 | Cite as

Dissipative holomorphic functions, Bloch radii, and the Schwarz Lemma

  • Lawrence A. Harris
  • Simeon Reich
  • David Shoikhet


Holomorphic Function Convex Domain Unique Fixed Point Numerical Range Complex Banach Space 
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  1. [1]
    D. Aharonov, S. Reich and D. Shoikhet,Flow invariance conditions for holomorphic mappings in Banach spaces, Math. Proc. Royal Irish Acad.99A (1999), 93–104.MATHMathSciNetGoogle Scholar
  2. [2]
    M. G. Crandall and T. M. Liggett,Generation of semigroups of nonlinear transformations on general Banach spaces, Amer. J. Math.93 (1971), 265–298.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    N. Dunford and J. T. Schwartz,Linear Operators, Part 1, Wiley, New York, 1957.Google Scholar
  4. [4]
    S. Dineen,The Schwarz Lemma, Clarendon Press, Oxford, 1989.MATHGoogle Scholar
  5. [5]
    C. J. Earle and R. S. Hamilton,A fixed point theorem for holomorphic mappings, inGlobal Analysis, Proc. Sympos. Pure Math. XVI, Amer Math. Soc., Providence, RI, 1970, pp. 61–65.Google Scholar
  6. [6]
    L. A. Harris,A continuous form of Schwarz's lemma in normed linear spaces, Pacific J. Math.38 (1971), 635–639.MATHMathSciNetGoogle Scholar
  7. [7]
    L. A. Harris,The numerical range of holomorphic functions in Banach spaces, Amer. J. Math.93 (1971), 1005–1019.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    L. A. Harris,On the size of balls covered by analytic transformations, Monatshefte Math.83 (1977), 9–23.MATHCrossRefGoogle Scholar
  9. [9]
    G. Lumer and R. S. Phillips,Dissipative operators in a Banach space, Pacific J. Math.11 (1961), 679–698.MATHMathSciNetGoogle Scholar
  10. [10]
    R. H. Martin, Jr.,Differential equations on a closed subsets of a Banach space, Trans. Amer. Math. Soc.179 (1973), 399–414.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    R. H. Martin, Jr.,Nonlinear Operators and Differential Equations in Banach Spaces, Wiley, New York, 1976.MATHGoogle Scholar
  12. [12]
    Z. Nehari,Conformal Mappings, McGraw-Hill, New York, 1952.Google Scholar
  13. [13]
    S. Reich,A nonlinear Hille-Yosida theorem in Banach spaces, J. Math. Anal. Appl.84 (1981), 1–5.MATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    S. Reich and D. Shoikhet,Generation theory for semigroups of holomorphic mappings in Banach spaces, Abstract and Applied Analysis1 (1996), 1–44.MATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    S. Reich and D. Shoikhet,Semigroups and generators on convex domains with the hyperbolic metric, Atti Accad. Naz. Lincei8 (1997), 231–250.MATHMathSciNetGoogle Scholar
  16. [16]
    J. T. Schwartz,Nonlinear Functional Analysis, Gordon and Breach, New York, 1969.MATHGoogle Scholar
  17. [17]
    K. Yosida,Functional Analysis, Springer, Berlin, 1971.MATHGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 2000

Authors and Affiliations

  • Lawrence A. Harris
    • 1
  • Simeon Reich
    • 2
  • David Shoikhet
    • 3
  1. 1.Mathematics DepartmentUniversity of KentuckyLexingtonUSA
  2. 2.Department of MathematicsThe Technion-Israel Institute of TechnologyHaifaIsrael
  3. 3.Department of Applied MathematicsInternational College of TechnologyKarmielIsrael

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