Bernstein’s theorem for the polydisc
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- by S. H. Tung PDF
- Proc. Amer. Math. Soc. 85 (1982), 73-76 Request permission
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.References
- Lars Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0203075
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
- S. H. Tung, Extension of Bernšteĭn’s theorem, Proc. Amer. Math. Soc. 83 (1981), no. 1, 103–106. MR 619992, DOI 10.1090/S0002-9939-1981-0619992-9
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 73-76
- MSC: Primary 32E30; Secondary 41A17
- DOI: https://doi.org/10.1090/S0002-9939-1982-0647901-6
- MathSciNet review: 647901