# Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems

## TL;DR

This paper extends classical Cauchy-Kowalevski and Holmgren theorems to infinite-dimensional settings using monomial expansions and Wiener space tools, broadening the scope of analytic PDE solutions.

## Contribution

It introduces infinite-dimensional versions of classical theorems by adapting the majorants method and employing Wiener space techniques.

## Key findings

- Established an infinite-dimensional Cauchy-Kowalevski theorem.
- Proved an infinite-dimensional Holmgren theorem.
- Extended classical PDE theorems to infinite variables.

## 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.