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Estimates for the uniform norm of complex polynomials in the unit disk
Author(s) -
Fournier Richard,
Letac Gérard,
Ruscheweyh Stephan
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910115
Subject(s) - mathematics , unit disk , norm (philosophy) , complex quadratic polynomial , complex plane , unit (ring theory) , polynomial , combinatorics , inequality , degree (music) , pure mathematics , mathematical analysis , law , mathematics education , physics , political science , acoustics
Let ‖ · ‖ denote the uniform norm in the unit disk of the complex plane ℂ. The main result in this note is as follows: For any complex polynomial P of degree at most n and any α ∈ ℂ the inequality‖ P ‖ ⩽ ( n + 1)(‖ z P ( z ) + α ‖ ‐ | α |)holds. For any α ≠ 0 the factor n + 1 is best possible, and we determine the cases of equality (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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