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The Stieltjes Moment Problem with Complex Exponents

✍ Scribed by Antonio J. Duran

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
835 KB
Volume
158
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In this paper, we characterize the complex sequences (z~n~)~n~ which satisfy the following condition: For each complex sequence (a~n~)~n~, there exists a function f such that the functions t^z^~n~f(t) are Lebesgue integrable and a~n~ = ∫ t^z^~n~f(t)(dt) for all n∫. In this case, we give for every sequence (a~n~)~n~ infinitely many C∫ functions f satisfying some growth conditions in x = 0 and x = + ∫, and such that a~n~ = ∫ t^z^~n~f(t)dt.

Finally, we extend this result for Banach space valued functions.

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