Guido Weiss: a few memories of a friend and an influential mathematician

TL;DR

This paper reflects on Guido Weiss's influential role in mathematics, focusing on spaces of homogeneous type, their evolution in pluricomplex analysis, and wavelet-based Littlewood-Paley analysis.

Contribution

It provides a survey of Guido Weiss's impact on the development of spaces of homogeneous type and their applications in analysis.

Findings

Spaces of homogeneous type are central in pluricomplex analysis.

Existence of weak factorization for spaces of holomorphic functions.

Construction of wavelet bases enables Littlewood-Paley analysis.

Abstract

This contribution starts with an exchange between us on the way we met Guido and he influenced our mathematical lives. Then it is mainly a survey paper that illustrates this influence by describing different topics and their subsequent evolution after his seminal papers and courses. Our main thread is the notion of a space of homogeneous type. In the second section we describe how it became central in pluricomplex analysis and consider particularly the existence of weak factorization for spaces of holomorphic functions. In the last section, one revisits the construction of a basis of wavelets in a space of homogeneous type and the way it allows a Littlewood-Paley analysis.