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arXiv · 1905.02109

Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems

Jiayang Yu·Xu Zhang
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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.

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Jiayang Yu, Xu Zhang. 2019-05-06. Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems. https://arxiv.org/abs/1905.02109

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