Minimality of Complex Exponential System

Abstract:

      A sufficient condition is obtained for the minimality of the complex exponential system $E(\Lambda, M)=\{z^l e^{\lambda_n z}:l=0,1,\ldots,m_n-1;\ n=1,2,\ldots\}$ in the Banach space $L^p_\alpha$ consisting of all functions $f$ such that $f^{-\alpha}\in L^p({\mathbb{R}})$. Moreover, if the incompleteness holds, each function in the closure of the linear span of exponential system $E(\Lambda, M)$ can be extended to an analytic function represented by a Taylor-Dirichlet series.