  In this work, we propose a convenient framework for infinite-dimensional
analysis (including real and complex analysis), 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 framework 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.
