Differentiability of Six Operators on Nonsmooth Functions and p-Variation
Differentiability of Six Operators on Nonsmooth Functions and p-Variation
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DOI：
10.1007/bfb0100744
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发表时间：
1999-07
期刊：
影响因子：
--
通讯作者：
R. Dudley;R. Norvaiša
中科院分区：
文献类型：
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作者：
R. Dudley;R. Norvaiša
这本书是关于可微的六个运营商的职能或对职能：组成（f的g），集成（的f dg），乘法和卷积的两个职能，都不同，以及产品的积分和逆运营商的一个职能。该算子关于p-变差范数是可微的，且具有最优余项界。因此，作为算子参数的函数可以是非光滑的，可能是不连续的，但六个算子中有四个对某些p-变分范数是解析的（全纯的）。读者将需要知道基本的真实的分析，包括黎曼和勒贝格积分。这本书是为分析师，统计学家和概率。分析师和统计学家都从不同的角度研究了一些算子的可微性，本卷试图统一和扩展他们的结果。
The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.