A Hausdorff-like moment problem and the inversion of the Laplace transform
https://doi.org/10.1002/mana.200510414Publisher, magazine: ,
Publication year: 2006
Lưu Trích dẫn Chia sẻAbstract
The problem of finding \(u\in{L^2(0,1)}\)satisfying \[ \int_0^1 u(x)x^{\alpha_k} dx=\mu_k, k=0,1,2,\dots \] is an ill-posed problem. The sequence of real distinct numbers \(\alpha_k\) is greater than \(-1/2\). The regularization of this problem is given, using solutions of the finite moment problem \[ \int_0^1 u(x)x^{\alpha_k} dx=\mu_k, k=0,1,2,\dots,n-1 \] and the orthogonal projections onto the space generated by orthogonal system of Müntz polynomials.
Tags: ill-posed problem; Müntz polynomial approximation; Hausdorff moment problem; regularization
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