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Polynomials with prescribed zeros and small norm. (English) Zbl 1174.26013
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.

MSC:
26C10Polynomials: location of zeros (real variables)
26D05Inequalities for trigonometric functions and polynomials
31A15Potentials and capacity, harmonic measure, extremal length (two-dimensional)