Generalization of a theorem of Carathéodory

Salvino Ciccariello, Antonio Cervellino

Carathéodory showed that $n$ complex numbers $c_1,...,c_n$ can uniquely be written in the form $c_p={\sum }_{j=1}^m{\rho }_j{{\epsilon }_j}^p$ with $p=1,...,n$, where the ${\epsilon }_j$s are different unimo…