Farthest-point norm conjecture for logarithmic-capacity continua

From papers

Let KCK\subset\mathbb{C} be compact and connected with more than one point. Let MKM_K be the smallest number such that, whenever pp has degree n1n\geq1 and p=p1pmp=p_1\cdots p_m,

j=1mpjKMKnpK.\prod_{j=1}^m\|p_j\|_K\leq M_K^n\|p\|_K.

Here K\|\cdot\|_K is the supremum norm on KK. Let L=[2,2]L=[-2,2]. Pritsker–Ruscheweyh extremal conjecture.

MKML.M_K\leq M_L.

The source attributes this natural extremal conjecture to Pritsker and Ruscheweyh and does not report a resolution.

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Sources & referencesView supporting material

Primary source

A. Baernstein, R. S. Laugesen and I. E. Pritsker, “Moment inequalities for equilibrium measures in the plane”, arXiv:math/0702456 (2007).

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