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)

[1] R. A. Silverman,et al. Special functions and their applications , 1966 .

[2] R. Gorenflo,et al. A Multi-Dimensional Hausdorff Moment Problem: Regularization by Finite Moments , 1999 .

[3] S. Saitoh,et al. Error estimates of the real inversion formulas of the laplace transform , 1998 .

[4] G. Talenti. Recovering a function from a finite number of moments , 1987 .

[5] Conditional Stability of a Real Inverse Formula for the Laplace Transform , 2001 .

[6] A Real Inversion Formula for the Laplace Transform , 1993 .

[7] Frank Stenger,et al. Complex variable and regularization methods of inversion of the Laplace transform , 1989 .

[8] E. Coddington. An Introduction to Ordinary Differential Equations , 1961 .

[9] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[10] Joseph A. Ball,et al. Reproducing Kernels and their Applications , 1999 .