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The Stieltjes moments problem for rapidly decreasing functions


Author: Antonio J. Duran
Journal: Proc. Amer. Math. Soc. 107 (1989), 731-741
MSC: Primary 44A60; Secondary 33A65, 44A10
DOI: https://doi.org/10.1090/S0002-9939-1989-0984787-0
MathSciNet review: 984787
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Abstract: We prove the following result: If $ {\left( {{a_n}} \right)_n}$ is a sequence of complex numbers, then there exists a $ {\mathcal{C}^\infty }$-function $ f$ such that $ f$ and all its derivatives are rapidly decreasing functions, $ f\left( t \right) = 0$ for $ t < 0$ and $ \int_0^{ + \infty } {{t^n}f\left( t \right)dt = {a_n}} $. We extend this result for a generalized Stieltjes moments problem. Also, we characterize the $ {C^\infty }$-functions $ f$ in $ \left( {0, + \infty } \right)$ such that $ f$ and all its derivatives are rapidly decreasing functions in $ \left( {0, + \infty } \right)$ and with null moments.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0984787-0
Keywords: Moments problem, rapidly decreasing functions
Article copyright: © Copyright 1989 American Mathematical Society

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