论文标题
关于拉普拉斯变换的反转（纪念dimitris gatzouras）
On the inversion of the Laplace transform (In Memory of Dimitris Gatzouras)
论文作者
论文摘要
Laplace Transform是一种有用且功能强大的分析工具，应用于应用数学的多个领域，包括微分方程，概率和统计。与傅立叶变换的反转类似，拉普拉斯变换的反转公式至关重要。这样的公式是古老的和众所周知的（傅里叶 - 梅林或布罗姆维奇的积分，后旁的倒置）。目前的工作是由基本统计问题激励的，即，从指数分布的随机样本的基本模型中对量表的参数函数的无偏估计。参数函数$ h（λ）$及其方差的均匀最小方差无偏估计器的形式以laguerre多项式和相应的傅立叶系数为序列，并且该结果的特定应用可产生laplace变换的新型反转公式。 MSC：主要44A10，62F10。 关键词和短语：指数分布，公正的估计；傅立叶局部系列；逆拉环变换；拉格雷多项式。
The Laplace transform is a useful and powerful analytic tool with applications to several areas of applied mathematics, including differential equations, probability and statistics. Similarly to the inversion of the Fourier transform, inversion formulae for the Laplace transform are of central importance; such formulae are old and well-known (Fourier-Mellin or Bromwich integral, Post-Widder inversion). The present work is motivated from an elementary statistical problem, namely, the unbiased estimation of a parametric function of the scale in the basic model of a random sample from exponential distribution. The form of the uniformly minimum variance unbiased estimator of a parametric function $h(λ)$, as well as its variance, are obtained as series in Laguerre polynomials and the corresponding Fourier coefficients, and a particular application of this result yields a novel inversion formula for the Laplace transform. MSC: Primary 44A10, 62F10. Key words and phrases: Exponential Distribution, Unbiased Estimation; Fourier-Laguerre Series; Inverse Laplace Transform; Laguerre Polynomials.
