标题： 调和分析与广义微分子代数中的自动连续性 显示英文标题

标题： Harmonic analysis and automatic continuity in the context of generalized differential subalgebras

摘要： 对于适当的参数$k,p,q$，我们引入并系统地研究了$(k,p,q)$-微分子代数类。 这是一个广泛的巴拿赫$^*$-代数类，由它们与$C^*$-包络的关系定义。 一些例子是由可赋范的双边$^*$-理想、闭合$^*$-导数的定义域、完整的希尔伯特代数以及各种类型的加权卷积代数给出的。 我们证明了这类代数具有各种有趣的性质，例如基于光滑函数的泛函演算下的闭性，$^*$-正则性，Wiener性质$(W)$，甚至自动连续性性质。 显示英文摘要

摘要： For appropriate parameters $k,p,q$, we introduce and systematically study the class of $(k,p,q)$-differential subalgebras. This is a vast class of Banach $^*$-algebras defined by their relation with their $C^*$-envelopes. Some examples are given by normable two-sided $^*$-ideals, domains of closed $^*$-derivations, full Hilbert algebras, and some weighted convolution algebras of various kinds. We prove that this class of algebras possesses various interesting properties, such as closedness under a functional calculus based on smooth functions, $^*$-regularity, Wiener's property $(W)$, and even properties of automatic continuity.