Beals characterization of pseudodifferential operators in Wiener spaces

TL;DR

This paper extends Beals' characterization to pseudodifferential operators in Wiener spaces, utilizing Wick bi-symbols and building on prior Calderón-Vaillancourt results to deepen understanding of infinite-dimensional analysis.

Contribution

It provides a Beals type characterization theorem for pseudodifferential operators specifically in Wiener spaces, using the Weyl calculus and Wick bi-symbols.

Findings

Establishes a Beals characterization in infinite-dimensional Wiener spaces

Defines pseudodifferential operators and symbols in this context

Highlights the role of Wick bi-symbols in the Weyl calculus

Abstract

The aim of this article is to prove a Beals type characterization theorem for pseudodifferential operators in Wiener spaces. The definition of pseudodifferential operators in Wiener spaces and a Calder\'on-Vaillancourt type result appear in [1]. The set of symbols considered here is the one of [1]. The Weyl calculus in infinite dimension considered here emphasizes the role of the Wick bi-symbols.