论文标题
关于无界功能划线的基本原理
On the Fundamental Principles of Unbounded Functional Calculi
论文作者
论文摘要
在本文中，提出了针对无界功能计算的新公理化，相关的理论是详细的，包括代数和拓扑性质的唯一性和兼容性结果和扩展定理。与较早的方法相反，对于基础代数，不需要做出通勤性假设。 在第二部分中，抽象理论在熟悉的情况下进行说明（部门操作员，半群生成器，正常运算符）。对于部门的演算和Hille-phillips-phillips微积分证明了新的拓扑扩展定理。此外，可以表明，部门运算符的Stieltjes和Hirsch演算是扇形计算的（小）拓扑扩展的亚库。
In this paper, a new axiomatization for unbounded functional calculi is proposed and the associated theory is elaborated comprising, among others, uniqueness and compatibility results and extension theorems of algebraic and topological nature. In contrast to earlier approaches, no commutativity assumptions need to be made about the underlying algebras. In a second part, the abstract theory is illustrated in familiar situations (sectorial operators, semigroup generators, normal operators). New topological extension theorems are proved for the sectorial calculus and the Hille--Phillips calculus. Moreover, it is shown that the Stieltjes and the Hirsch calculus for sectorial operators are subcalculi of a (small) topological extension of the sectorial calculus.
