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math.CA2008★ 5 cited
New estimates for the length of the Erdos-Herzog-Piranian lemniscate
Alexander Fryntov, Fedor Nazarov
Let p(z) be a monic polynomial of degree n. Consider the lemniscate L={z:|p(z)|=1}. It has been conjectured that L has the largest length when p(z)=z^n-1. We show that the length o…
math.CA2002
Lower bounds for quasianalytic functions, I. How to control smooth functions?
F. Nazarov, M. Sodin, A. Volberg
Consider a class of functions of one real variable with the following uniqueness property: if a function f(x) from the class vanishes on a set of positive measure, then f is the ze…