Non Commutative Functional Calculus: Bounded Operators

Fabrizio Colombo; Graziano Gentili; Irene Sabadini; Daniele C. Struppa

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Non Commutative Functional Calculus: Bounded Operators

机译：非交换函数演算：有界算子

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摘要

In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the new notion of slice-regularity, see Gentili and Struppa (Acad Sci Paris 342:741-744, 2006) and the key tools are a new resolvent operator and a new eigenvalue problem.

机译：在本文中，我们为四元数Banach空间上定义的有界算子开发了一个功能演算。该演算基于切片规则性的新概念（请参见Gentili和Struppa（Acad Sci Paris 342：741-744，2006年）），关键工具是一个新的分解算子和一个新的特征值问题。

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来源
《Complex analysis and operator theory》 |2010年第4期|共23页
作者
Fabrizio Colombo; Graziano Gentili; Irene Sabadini; Daniele C. Struppa;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Functional calculus; Spectral theory; Bounded operators;

机译：功能演算;谱理论;有界算子;

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专利

1. Non Commutative Functional Calculus: Bounded Operators [J] . Fabrizio Colombo, Graziano Gentili, Irene Sabadini, Complex analysis and operator theory . 2010,第4期

机译：非交换函数演算：有界算子
2. Non-commutative functional calculus: Unbounded operators [J] . Colombo F, Gentili G, Sabadini I, Journal of geometry and physics . 2010,第2期

机译：非交换函数演算：无界算子
3. Functional Calculus of Operators with Heat Kernel Bounds on Non-Doubling Manifolds with Ends [J] . The Anh Bui, Xuan Thinh Duong, Li Ji, Indiana University Mathematics Journal . 2020,第3期

机译：与末端非加倍歧管的热核界限的运营商功能微积分
4. Functional calculus on algebras of operators generated by a self-adjoint operator in Pontryagin space ∏_1 [C] . Vladimir I. Chilin, Sofya S. Masharipova International Conference on Topological Algebras and their Applications . 2018

机译：在Pontryagin空间空间π_1中自伴随算子生成的运算符代数的功能微积分
5. A FUNCTIONAL CALCULUS FOR NON-COMMUTATIVE SELF-ADJOINT OPERATORS [D] . ANDERSON, ROBERT F. V. -1

机译：非通信自伴算子的功能计算
6. A linear-time algorithm that avoids inverses and computes Jackknife (leave-one-out) products like convolutions or other operators in commutative semigroups [O] . John L. Spouge, Joseph M. Ziegelbauer, Mileidy Gonzalez 2020

机译：一种线性时间算法可避免逆转和计算换乘器或其他操作员的jackknife（休留一张）产品
7. Non commutative functional calculus: bounded operators [O] . Colombo, F., Gentili, G., Sabadini, I., 2007

机译：非交换函数演算：有界算子
8. Formulae and Bounds connected to Optimal Design and Homogenization of Partial Differential Operators and Integral Functionals [R] . Lukkassen, D. 1996

机译：与偏微分算子和积分泛函的优化设计和均匀化相关的公式和界

Non Commutative Functional Calculus: Bounded Operators

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