Noncommutative Functional Calculus
Noncommutative Functional Calculus
复制标题
DOI：
10.1007/978-3-0348-0110-2
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
F. Colombo;I. Sabadini;D. Struppa
中科院分区：
文献类型：
--
作者：
F. Colombo;I. Sabadini;D. Struppa
本书介绍了不一定可交换线性算子的 n 元组的函数演算。特别是，开发了四元数线性算子的函数微积分。这些演算基于 Clifford 代数中具有值的函数的新超全纯理论：书中详细描述了所谓的切片单基因函数。对于具有四元数代数中的值的函数，这些函数被称为切片正则函数。除附录和引言外，所有结果都是新的，并且首次出现在专着中。该材料经过精心准备，尽可能独立。目标受众包括对算子理论、谱理论、超复杂分析和数学物理感兴趣的研究人员、研究生和研究生。
This book presents a functional calculus for n-tuples of not necessarily commuting linear operators. In particular, a functional calculus for quaternionic linear operators is developed. These calculi are based on a new theory of hyperholomorphicity for functions with values in a Clifford algebra: the so-called slice monogenic functions which are carefully described in the book. In the case of functions with values in the algebra of quaternions these functions are named slice regular functions. Except for the appendix and the introduction all results are new and appear for the first time organized in a monograph. The material has been carefully prepared to be as self-contained as possible. The intended audience consists of researchers, graduate and postgraduate students interested in operator theory, spectral theory, hypercomplex analysis, and mathematical physics.