Dense of Rational Combinations of {e(-iλnt} in C[a,b]

Abstract:

      The present paper investigates approximation by rational combinations of {x^λ_n} for a complex sequence {λ_n} ,As an application,we have an interesting result in general trigonometric polynomials case, that is,for a real monotone sequence satisfying (?)△λ_n= l, the ratio-nal combination of {e^(-iλ_nt} are dense in C_[a,b] for any a,b-∞＜a＜b＜∞，if and only if l=0.