Abstract

We prove uniqueness for the nonharmonic trigonometric series k=0akeiλkx under the weaker condition (*) where k=0ak/expλkγ<, for some 0 < γ < 1. In other words, if {λk}0 satisfies the above condition (*), and if k=0akeiλkx=0, then ak = 0 for all k = 0, 1,…. Finally, we state an improvement of Zygmund's uniqueness result as a corollary.

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