An Extension of the Hirsch Symbolic Calculus
An Extension of the Hirsch Symbolic Calculus
复制标题
赫希符号演算的扩展
DOI：
--
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
M. Sanz
中科院分区：
文献类型：
--
作者：
C. Martínez;M. Sanz
由弗朗西斯·赫希（Francis Hirsch）（在1972年至1976年的几篇论文中）开发的符号演算已经是一个经典的理论，它引入并研究了与Banach空间上的非负线性算子A和Radon测度μ的Stieltjes变换f相关联的算子f（A）。要求算子A有一个稠密域，并且测度μ和值f（∞））是真实的且非负的。这三个条件在主要结果的证明中是必不可少的，但它们的限制性很强，因为重要的情况被排除了，如复指数α的分数幂Aα，或基A的分数幂A α是非稠密定义的。在本文中，我们提出了一个重建的赫希理论，而不使用这些假设。
The symbolic calculus developed by Francis Hirsch (in several papers, between 1972 and 1976) is an already classical theory that introduces and studies the operators f(A) associated to a non-negative linear operator A on a Banach space and to the Stieltjes transform f of a Radon measure μ. It is required that the operator A has a dense domain and that the measure μ, as well as the value f(∞)), are real and non-negative. These three conditions are essential in the proof of the main results, but they are very restrictive, since important cases are excluded, as the fractional powers Aα of complex exponent α, or of base A non-densely defined. In this paper we present a reconstruction of the Hirsch theory, without using those hypothesis.