The Michigan Mathematical Journal

Semigroups of holomorphic self-maps of domains and one-parameter semigroups of isometries of Bergman spaces

William Hornor

Full-text: Open access

Article information

Michigan Math. J., Volume 51, Issue 2 (2003), 305-326.

First available in Project Euclid: 4 August 2003

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B33: Composition operators 47D03: Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20} 32A36: Bergman spaces
Secondary: 30H05: Bounded analytic functions


Hornor, William. Semigroups of holomorphic self-maps of domains and one-parameter semigroups of isometries of Bergman spaces. Michigan Math. J. 51 (2003), no. 2, 305--326. doi:10.1307/mmj/1060013198.

Export citation


  • M. Abate, The infinitesimal generators of semigroups of holomorphic maps, Ann. Mat. Pura Appl. (4) 161 (1992), 167--180.
  • H. Amann, Ordinary differential equations: An introduction to nonlinear analysis, de Gruyter, New York, 1990.
  • E. Berkson, One-parameter semigroups of isometries into $H^p,$ Pacific J. Math. 86 (1980), 403--413.
  • E. Berkson and H. Porta, Hermitian operators and one-parameter groups of isometries in Hardy spaces, Trans. Amer. Math. Soc. 185 (1973), 331--344.
  • ------, Semigroups of analytic functions and composition operators, Michigan Math. J. 25 (1978), 101--115.
  • J. Cima and W. Wogen, Unbounded composition operators on $H^2(B_2),$ Proc. Amer. Math. Soc. 99 (1987), 477--483.
  • J. B. Conway, A course in functional analysis, Springer-Verlag, New York, 1985.
  • C. Cowen and B. MacCluer, Composition operators on spaces of analytic functions, CRC Press, Boca Raton, FL, 1995.
  • K. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, Springer-Verlag, New York, 2000.
  • H. Grauert and R. Remmert, Theory of Stein spaces, Springer-Verlag, New York, 1979.
  • R. Gunning, Introduction to holomorphic functions of several variables, vol. I, Brooks/Cole, Pacific Grove, CA, 1990.
  • P. Henrici, Applied and computational complex analysis, vol. II, Wiley, New York, 1977.
  • C. Kolaski, Isometries of Bergman spaces over bounded Runge domains, Canad. J. Math. 33 (1981), 1157--1164.
  • B. MacCluer and J. Shapiro, Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad. J. Math. 38 (1986), 878--906.
  • A. Pazy, Semigroups of linear operators and applications to partial differential equations, Appl. Math. Sci., 44, Springer-Verlag, New York, 1983.
  • W. Rudin, Functional analysis, McGraw-Hill, New York, 1973.
  • J. Shapiro, Composition operators and classical function theory, Springer-Verlag, New York, 1993.
  • R. Singh and J. Manhas, Composition operators on function spaces, North-Holland, Amsterdam, 1993.
  • A. Siskakis, Semigroups of composition operators in Bergman spaces, Bull. Austral. Math. Soc. 35 (1987), 397--406.
  • ------, Semigroups of composition operators on spaces of analytic functions, a review, Studies on composition operators (Laramie, WY, 1996), Contemp. Math., 213, pp. 229--252, Amer. Math. Soc., Providence, RI, 1998.
  • J. Weidmann, Linear operators in Hilbert spaces, Springer-Verlag, New York, 1980.
  • W. Wogen, The smooth mappings which preserve the Hardy space $H^2_B_n},$ Contributions to operator theory and its applications (Mesa, AZ, 1987), Oper. Theory: Adv. Appl., 35, pp. 249--263, Birkhäuser, Basel, 1988.