This website requires JavaScript.

Quaternionic resolvent equation and series expansion of the $\mathcal{S}$-resolvent operator

Riccardo GhiloniVincenzo Recupero
Feb 2024
0被引用
0笔记
摘要原文
In the present paper, we prove a resolvent equation for the $\mathcal{S}$-resolvent operator in the quaternionic framework. Exploiting this resolvent equation, we find a series expansion for the $\mathcal{S}$-resolvent operator in an open neighborhood of any given quaternion belonging to the $\mathcal{S}$-resolvent set. Some consequences of the series expansion are deduced. In particular, we describe a property of the geometry of the $\mathcal{S}$-resolvent set in terms of the Cassini pseudo-metric on quaternions. The concept of vector-valued real analytic function of several variables plays a crucial role in the proof of the mentioned series expansion for the $\mathcal{S}$-resolvent operator.
展开全部
机器翻译
AI理解论文&经典十问
图表提取
参考文献
发布时间 · 被引用数 · 默认排序
被引用
发布时间 · 被引用数 · 默认排序
社区问答