Roger Godement et les fonctions de type positif

TL;DR

This paper explores the early history of positive-definite functions, highlighting Roger Godement's contributions and including historical correspondence related to his 1946 thesis.

Contribution

It provides historical context and personal insights into the development of positive-definite functions, emphasizing Godement's role and original ideas before 1950.

Findings

Historical overview of positive-definite functions before 1950

Includes original letters by Roger Godement

Highlights Godement's influence on the field

Abstract

Ce texte, \'ecrit pour la Gazette de la Soci\'et\'e math\'ematique de France, \'evoque les fonctions de type positif et leur histoire avant 1950 ; on y pr\'esente notamment des extraits de lettres \'ecrites par Roger Godement, qui leur consacra sa th\`ese en 1946. This is an expository paper on the early history of positive-definite functions, written for the "Gazette de la Soci\'et\'e Math\'ematique de France". It contains pictures of letters written by Roger Godement, during and after the preparation of his 1946 thesis about positive-definite functions on groups.