Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems

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...

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Bibliographic Details
Published in:Science China. Mathematics 2019-09, Vol.62 (9), p.1645-1656
Main Authors: Yu, Jiayang, Zhang, Xu
Format: Article
Language:English
Subjects:
Applications of Mathematics
Brief Reports
Mathematical analysis
Mathematics
Mathematics and Statistics
Theorems
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Summary: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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-019-9539-y