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A Hausdorff-like moment problem and the inversion of the Laplace transform

✍ Scribed by Nguyen Dung; Nguyen Vu Huy; Pham Hoang Quan; Dang Duc Trong

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 159 KB
Volume: 279
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200510414

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✦ Synopsis

Abstract

We consider the problem of finding u ∈ L ^2^(I ), I = (0, 1), satisfying

∫~I~ u (x )x d__x__ = μ ~k~ ,

where k = 0, 1, 2, …, (α ~k~ ) is a sequence of distinct real numbers greater than –1/2, and μ = (μ ~kl~ ) is a given bounded sequence of real numbers. This is an ill‐posed problem. We shall regularize the problem by finite moments and then, apply the result to reconstruct a function on (0, +∞) from a sequence of values of its Laplace transforms. Error estimates are given. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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