正则代数$L_p^w(G)$的构造
Constructions of regular algebras $L_p^w(G)$
摘要：
局部紧阿贝尔群$G$上的加权代数$L_1^w(G)$的（Shilov）正则性的判别法由Beurling（1949）和Domar（1956）的工作已知。本文将这一判据推广到平移不变加权代数$L_p^w(G)$，并给出了$p>1$ .正则代数$L_p^w(G)$构造在任意σ紧阿贝尔群$G$上.作者以前证明了σ-紧性对于具有$p>1$的加权代数$L_p^w(G)$的存在性是必要的（在交换情形下）。
英文摘要：
Criterion of (Shilov) regularity for weighted algebras $L_1^w(G)$ on a locally compact abelian group $G$ is known by works of Beurling (1949) and Domar (1956). In the present paper this criterion is extended to translation invariant weighted algebras $L_p^w(G)$ with $p>1$. Regular algebras $L_p^w(G)$ are constructed on any sigma-compact abelian group $G$. It was proved earlier by the author that sigma-compactness is necessary (in the abelian case) for the existence of weighted algebras $L_p^w(G)$ with $p>1$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
