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The location of critical points of finite Blaschke products
Author:
David A. Singer
Journal:
Conform. Geom. Dyn. 10 (2006), 117-124
MSC (2000):
Primary 53A35; Secondary 30D50
Posted:
June 7, 2006
MathSciNet review:
2223044
Full-text PDF Free Access
Abstract |
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Abstract: A theorem of Bôcher and Grace states that the critical points of a cubic polynomial are the foci of an ellipse tangent to the sides of the triangle joining the zeros. A more general result of Siebert and others states that the critical points of a polynomial of degree  are the algebraic foci of a curve of class  which is tangent to the lines joining pairs of zeroes. We prove the analogous results for hyperbolic polynomials, that is, for Blaschke products with  roots in the unit disc.
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Additional Information
David A. Singer
Affiliation:
Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106-7058
Email:
david.singer@case.edu
DOI:
http://dx.doi.org/10.1090/S1088-4173-06-00145-7
PII:
S 1088-4173(06)00145-7
Received by editor(s):
January 16, 2006
Posted:
June 7, 2006
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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