On multivariate quasipolynomials of the minimal deviation from zero (Q5959028)

The main result of the paper gives a rather precise upper and lower estimates of the least deviation \(\inf_R\max_{0\leq x,y\leq 1}|R(x,y) |\) where \(R\) runs over all quasipolynomials \(\sum^m_{i=0} \sum^n_{j=0} \alpha_{ij}^{(m,n)} x^{\mu_i}y^{\nu_j}\) with prescribed exponents \(0\leq\mu_0 < \mu_1< \cdots< \mu_m\), \(0\leq\nu_0 <\nu_1< \cdots< \nu_n\) and \(\alpha_{mn}^{(m, n)} =1\) (monic quasipolynomials of a fixed spectrum).