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UNIQUENESS OF A NONHARMONIC TRIGONOMETRIC SERIES UNDER AN EXPONENTIAL GROWTH CONDITION
Published online by Cambridge University Press: 18 April 2001
Abstract
We prove uniqueness for the nonharmonic trigonometric series [sum ]∞k=0akeiλkx under the weaker condition (*) where [sum ]∞k=0 [mid ]ak[mid ]/exp[mid ]λk[mid ]γ < ∞, for some 0 < γ < 1. In other words, if {λk}∞0 satisfies the above condition (*), and if [sum ]∞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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- © The London Mathematical Society 2001
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