6 papers · 1 filter
Measures on General Codimensional Surfaces in Infinite Dimensions and Stokes-Type Theorems
Zhouzhe Wang, Jiayang Yu, Xu Zhang
In this paper, we give an explicit construction of surface measures on a class of surfaces with arbitrary, possibly infinite, codimension in . These measures are constructe…
Sobolev spaces in infinite dimensions
Zhouzhe Wang, Jiayang Yu, Xu Zhang +2
The classical theory of Sobolev spaces in finite dimensions is well established. Because infinite-dimensional spaces possess inherent analytical and topological complexities, devel…
A convenient setting for infinite-dimensional analysis
Jiayang Yu, Xu Zhang
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 so…
estimates and existence theorems for the operators in infinite dimensions, II
Zhouzhe Wang, Jiayang Yu, Xu Zhang
This paper is the second part of our series of works to establish estimates and existence theorems for the operators in infinite dimensions. In this par…
estimates and existence theorems for the operators in infinite dimensions, I
Jiayang Yu, Xu Zhang
The classical estimate for the operators is a basic tool in complex analysis of several variables. Naturally, it is expected to extend this estimate to…
Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems
Jiayang Yu, Xu Zhang
The aim of this paper is to show Cauchy-Kowalevski and Holmgren type theorems with infinite number of variables. We adopt von Koch and Hilbert's definition of analyticity of functi…