Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems

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.