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Zbl 1174.26013
Totik, Vilmos; Varjú, Péter P.
Polynomials with prescribed zeros and small norm. (English)
[J] Acta Sci. Math. 73, No. 3-4, 593-611 (2007). ISSN 0001-6969

The authors derive lower and upper bounds on the supremum norm of a univariate polynomial when some of its zeros lie on the unit circle. They also provide examples of polynomials showing that the bounds are tight. Two different technical constructions are used to show the main results, both relying on the logarithmic potential of measure theory.
[Didier Henrion (Toulouse)]

MSC 2000:: *26C10 Polynomials: location of zeros (real variables)
26D05 Inequalities for trigonometric functions and polynomials
31A15 Potentials, etc. (two-dimensional)

Keywords: polynomials; location of roots; analytic theory

Cited in: Zbl 1240.30026

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