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Proceedings of the American Mathematical Society

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



Bernstein's theorem for the polydisc

Author: S. H. Tung
Journal: Proc. Amer. Math. Soc. 85 (1982), 73-76
MSC: Primary 32E30; Secondary 41A17
MathSciNet review: 647901
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Abstract: A well-known theorem of Bernstein states that if a polynomial of degree $ N$ of a complex variable has its modulus no larger than one on the unit disc then the modulus of its derivative will not exceed $ N$ on the unit disc. The result has been extended to the case of polynomials on the unit ball in several complex variables. Here we generalize the theorem to the cases of the unit polydisc and the unit polycylinder which is a topological product of a unit ball and a unit polydisc.

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Keywords: Bernstein's theorem, polynomial, polydisc, polycylinder
Article copyright: © Copyright 1982 American Mathematical Society