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UNIQUENESS OF A NONHARMONIC TRIGONOMETRIC SERIES UNDER AN EXPONENTIAL GROWTH CONDITION

Published online by Cambridge University Press:  18 April 2001

HEE JUNG KIM ,
SOON-YEONG CHUNG  and
DOHAN KIM
HEE JUNG KIM
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151–742, Korea
SOON-YEONG CHUNG
Affiliation:
Department of Mathematics, Sogang University, Seoul 121–742, Korea
DOHAN KIM
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151–742, Korea
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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.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 2 , March 2001 , pp. 199 - 202
Copyright
© The London Mathematical Society 2001

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