无限维分析的便利框架
A convenient setting for infinite-dimensional analysis
AI总结：
本文针对无限维分析提出便利框架，简化微分积分操作与分部积分条件，推广欧氏空间卷积性质，且与有限维分析联系更清晰，更适用于计算及相关问题研究。
摘要：
本文提出一个适用于无限维分析（含实与复无限维分析）的便利框架，其中可轻松执行微分（弱意义下）与积分运算，在较弱条件下方便建立分部积分，尤其欧氏空间中卷积的良好性质与结果可通过取极限在某种意义下推广至无限维空间。相比现有无限维分析工具，本框架与有限维分析的联系更便利清晰，因此更适合计算及研究无限维空间中的分析问题。
英文摘要：
In this work, we propose a convenient framework for infinite-dimensional analysis (including both real and complex analysis in infinite dimensions), in which differentiation (in some weak sense) and integration operations can be easily performed, integration by parts can be conveniently established under rather weak conditions, and especially some nice properties and consequences obtained by convolution in Euclidean spaces can be extended to infinite-dimensional spaces in some sense by taking the limit. Compared to the existing tools in infinite-dimensional analysis, our setting enjoys more convenient and clearer links with that of finite dimensions, and hence it is more suitable for computation and studying some analysis problems in infinite-dimensional spaces.
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。
