A necessary and sufficient condition is obtained for the incompleteness of complex exponential system in the weighted Banach space Lαp = {f:∫+∞∞ |f(t)e-α(t)|pdt < +∞},where 1 ≤ p < +∞ and α(t) is a weight on R.
A sufficient condition is obtained for the minimality of the complex exponential system E(Λ,M) = {z l e λ n z : l = 0,1,...,m n - 1;n = 1,2,...} in the Banach space L p α consisting of all functions f such that f-α∈ L p (R).Moreover,if the incompleteness holds,each function in the closure of the linear span of exponential system E(Λ,M) can be extended to an analytic function represented by a Taylor-Dirichlet series.
