  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.
