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October, 2003 Every Stieltjes moment problem has a solution in Gel'fand-Shilov spaces
Jaeyoung CHUNG, Soon-Yeong CHUNG, Dohan KIM
J. Math. Soc. Japan 55(4): 909-913 (October, 2003). DOI: 10.2969/jmsj/1191418755

Abstract

We prove that every Stieltjes problem has a solution in Gel'fand-Shilov spaces Sβ for every β>1. In other words, for an arbitrary sequence {μn} there exists a function ϕ in the Gel'fand-Shilov space Sβ with support in the positive real line whose moment 0xnϕ(x)dx=μn for every nonnegative integer n.

This improves the result of A. J. Duran in 1989 very much who showed that every Stieltjes moment problem has a solution in the Schwartz space S, since the Gel'fand-Shilov space is much a smaller subspace of the Schwartz space. Duran's result already improved the result of R. P. Boas in 1939 who showed that every Stieltjes moment problem has a solution in the class of functions of bounded variation. Our result is optimal in a sense that if β1 we cannot find a solution of the Stieltjes problem for a given sequence.

Citation

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Jaeyoung CHUNG. Soon-Yeong CHUNG. Dohan KIM. "Every Stieltjes moment problem has a solution in Gel'fand-Shilov spaces." J. Math. Soc. Japan 55 (4) 909 - 913, October, 2003. https://doi.org/10.2969/jmsj/1191418755

Information

Published: October, 2003
First available in Project Euclid: 3 October 2007

zbMATH: 1046.44004
MathSciNet: MR2003751
Digital Object Identifier: 10.2969/jmsj/1191418755

Subjects:
Primary: 44A60
Secondary: 46F15

Keywords: existence , Gel'fand-Shilov space , Stieltjes moment problem

Rights: Copyright © 2003 Mathematical Society of Japan

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Vol.55 • No. 4 • October, 2003
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