2019/05/06 by Jiayang Yu, Xu Zhang, Yu, Jiayang +1
Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.1905.02109
openalex publication_date 2019/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.