Generalizations of Müntz’s Theorem via a Remez-type inequality for Müntz spaces
Generalizations of Müntz’s Theorem via a Remez-type inequality for Müntz spaces
The principal result of this paper is a Remez-type inequality for Müntz polynomials: \begin{equation*}p(x) := \sum ^{n}_{i=0} a_{i} x^{\lambda _{i}}, \end{equation*} or equivalently for Dirichlet sums: \begin{equation*}P(t) := \sum ^{n}_{i=0}{a_{i} e^{-\lambda _{i} t}} ,\end{equation*} where $0 = \lambda _{0} < \lambda _{1} < \lambda _{2} <\cdots$. The most useful form …