论文信息 - A Hausdorff‐like moment problem and the inversion of the Laplace transform

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

We consider the problem of finding u ∈ L2(I ), I = (0, 1), satisfying ∫Iu (x )x dx = μk, where k = 0, 1, 2, …, (αk) is a sequence of distinct real numbers greater than –1/2, and μ = (μkl) 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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