Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（9）
• 页码范围: 1645-1656
• 页数: 12页
• 语种: 英文

摘要

The aim of this paper is to show Cauchy-Kowalevski and Holmgren type theorems with an 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.