Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Some characterizations of semi-Bloch functions


Authors: Rauno Aulaskari and Peter Lappan
Journal: Proc. Amer. Math. Soc. 119 (1993), 1233-1238
MSC: Primary 30D45
DOI: https://doi.org/10.1090/S0002-9939-1993-1165046-3
MathSciNet review: 1165046
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A function $ f$ analytic in the unit disk is called a semi-Bloch function if, for each complex number $ \lambda $, the function $ {g_\lambda }(z) = \exp (\lambda f(z))$ is a normal function. We give both an analytic and a geometric characterization of semi-Bloch functions, together with some examples to show that semi-Bloch functions are not closed under either addition or multiplication.


References [Enhancements On Off] (What's this?)

  • [1] L. V. Ahlfors, Zur Theorie der Überlagerungsflächen, Acta Math. 65 (1935), 157-194. MR 1555403
  • [2] J. M. Anderson, J. Clunie, and Ch. Pommerenke, On Bloch functions and normal functions, J. Reine Angew. Math. 270 (1974), 12-37. MR 0361090 (50:13536)
  • [3] S. Axler, The Bergman space, the Bloch space, and commutators of multiplication operators, Duke Math. J. 53 (1986), 315-332. MR 850538 (87m:47064)
  • [4] F. Colonna, Bloch and normal functions and their relation, Rend. Circ. Mat. Palermo (2) 38 (1989), 161-180. MR 1029707 (91b:30102)
  • [5] P. Lappan, A criterion for a meromorphic function to be normal, Comment. Math. Helv. 49 (1974), 492-495. MR 0379850 (52:755)
  • [6] O. Lehto and K. I. Virtanen, Boundary behaviour and normal meromorphic functions, Acta Math. 97 (1957), 47-65. MR 0087746 (19:403f)
  • [7] K. F. Tse, On the sums and products of normal functions, Comment Math. Univ. St. Paul. 17 (1969), 63-72. MR 0268385 (42:3283)
  • [8] M. Tsuji, Potential theory in modern function theory, Maruzen, Tokyo, 1959. MR 0114894 (22:5712)
  • [9] L. Zalcman, A heuristic principle in complex function theory, Amer. Math. Monthly 82 (1975), 813-817. MR 0379852 (52:757)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30D45

Retrieve articles in all journals with MSC: 30D45


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1165046-3
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society