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)

 
 

 

A note on the zeros of Faber polynomials


Author: A. W. Goodman
Journal: Proc. Amer. Math. Soc. 49 (1975), 407-410
MSC: Primary 30A08
DOI: https://doi.org/10.1090/S0002-9939-1975-0367167-0
MathSciNet review: 0367167
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: By an elementary counterexample we show that a conjecture about the zeros of the Faber polynomials is false.


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

  • [1] J. H. Curtiss, Faber polynomials and the Faber series, Amer. Math. Monthly 78 (1971), 577-596. MR 45 #2183. MR 0293104 (45:2183)
  • [2] G. Faber, Über polynomische Entwickelungen, Math. Ann. 57 (1903), 389-408. MR 1511216
  • [3] A. W. Goodman, The rotation theorem for starlike univalent functions, Proc. Amer. Math. Soc. 4 (1953), 278-286. MR 14, 739. MR 0053221 (14:739g)
  • [4] T. Kövari and C. Pommerenke, On Faber polynomials and Faber expansions, Math. Z. 99 (1967), 193-206. MR 37 #3013. MR 0227429 (37:3013)
  • [5] A. I. Markuševič, Theory of analytic functions, GITTL, Moscow, 1950; English transl. in three volumes, Vol. III, Prentice-Hall, Englewood Cliffs, N. J., 1967. MR 38 #304.
  • [6] J. L. Ullman, The location of the zeros of the derivatives of Faber polynomials, Proc. Amer. Math. Soc. 34 (1972), 422-424. MR 45 #8809. MR 0299761 (45:8809)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A08

Retrieve articles in all journals with MSC: 30A08


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0367167-0
Keywords: Faber polynomials, zeros of Faber polynomials
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society