A Hausdorff‐like moment problem and the inversion of the Laplace transform
Copyright policy )A Hausdorff‐like moment problem and the inversion of the Laplace transform
AbstractWe consider the problem of finding u ∈ L 2(I ), I = (0, 1), satisfying ∫I u (x )x dx = 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)
regularization, Müntz polynomial approximation, Laplace transform, Moment problems, Hausdorff moment problem, ill-posed problem, Numerical methods for integral transforms, Numerical methods for ill-posed problems for integral equations
regularization, Müntz polynomial approximation, Laplace transform, Moment problems, Hausdorff moment problem, ill-posed problem, Numerical methods for integral transforms, Numerical methods for ill-posed problems for integral equations
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