Balancing Polynomials in the Chebyshev Norm

Victor Reis

Given $n$ polynomials $p_1,\dots ,p_n$ of degree at most $n$ with $\Vert p_i{\Vert }_{\infty }\le 1$ for $i\in [n]$, we show there exist signs $x_1,\dots ,x_n\in \{-1,1\}$ so that \[\Big\|…