C⁎玻上的微分算子及其在切线群上的平滑函数微积分和施瓦茨函数中的应用

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-07-31 DOI:10.1016/j.jfa.2024.110615

Omar Mohsen

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引用次数: 0

摘要

我们引入了-代数上微分算子的概念。它是光滑流形上微分算子的非交换类似物。我们证明了所有微分算子的共同闭域在光滑函数微积分下是封闭的。作为推论，我们证明康内切群上的施瓦茨函数在光滑函数微积分下是封闭的。

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Differential operators on C⁎-algebras and applications to smooth functional calculus and Schwartz functions on the tangent groupoid

We introduce the notion of a differential operator on $C^{⁎}$ -algebras. This is a noncommutative analogue of a differential operator on a smooth manifold. We show that the common closed domain of all differential operators is closed under smooth functional calculus. As a corollary, we show that Schwartz functions on Connes tangent groupoid are closed under smooth functional calculus.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis