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.
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.
基金
supported by National Natural Science Foundation of China(Grant No.11501384)
supported by National Natural Science Foundation of China(Grant No.11221101)
the NSFC-CNRS Joint Research Project(Grant No.11711530142)
the Program for Changjiang Scholars and Innovative Research Team in University from the Chinese Education Ministry(Grant No.IRT 16R53)
