LAUSR

Abstract In this paper we consider a generalized trigonometric moment problem in a weighted L 2 ( − ∞ , 0 ) space. We obtain a solution which is in the closed span of some exponential system E Λ = { t k e i λ n t } in the weighted space. Our motivation is a classical trigonometric moment problem in L 2 ( − π , π ) . Based on an entire function, a lower bound for the distance between exponential functions and the closed span of the remaining elements of the system E Λ is derived. An upper bound is then obtained for the norm of the elements of a biorthogonal system to E Λ . The proof of our result utilizes the notions of Bessel sequences and Riesz-Fischer sequences.