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

Dung Nguyen | Zendy; Huy Nguyen Vu | Zendy; Quan Pham Hoang | Zendy; Trong Dang Duc | Zendy

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

Author(s) -

Dung Nguyen,

Huy Nguyen Vu,

Quan Pham Hoang,

Trong Dang Duc

Publication year - 2006

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200510414

Subject(s) - mathematics , laplace transform , sequence (biology) , bounded function , moment problem , hausdorff space , moment (physics) , inversion (geology) , real number , inverse laplace transform , combinatorics , function (biology) , mathematical analysis , pure mathematics , statistics , paleontology , genetics , physics , classical mechanics , structural basin , evolutionary biology , principle of maximum entropy , biology

We consider the problem of finding u ∈ L 2 ( I ), I = (0, 1), satisfying∫ I u ( x ) x α kd 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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