Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems
Functional Analysis
2019-05-07 v1
Abstract
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 functions as monomial expansions. Our Cauchy-Kowalevski type theorem is derived by modifying the classical method of majorants. Based on this result, by employing some tools from abstract Wiener spaces, we establish our Holmgren type theorem.
Cite
@article{arxiv.1905.02109,
title = {Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems},
author = {Jiayang Yu and Xu Zhang},
journal= {arXiv preprint arXiv:1905.02109},
year = {2019}
}
Comments
12 pages. This paper has been accepted for publication in SCIENCE CHINA Mathematics