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Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems

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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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Acknowledgements

The first author was supported by National Natural Science Foundation of China (Grant No. 11501384). The second author was supported by National Natural Science Foundation of China (Grant No. 11221101), the NSFC-CNRS Joint Research Project (Grant No. 11711530142) and the PCSIRT from the Chinese Education Ministry (Grant No. IRT_16R53).

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  1. School of Mathematics, Sichuan University, Chengdu, 610064, China

    Jiayang Yu & Xu Zhang

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  1. Jiayang Yu
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  2. Xu Zhang
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Correspondence to Xu Zhang.

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Yu, J., Zhang, X. Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems. Sci. China Math. 62, 1645–1656 (2019). https://doi.org/10.1007/s11425-019-9539-y

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