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He contributed to probability, functional analysis, partial differential equations and series. He also studied geometry. In 1926 he extended Laplace transforms to broader function classes. He undertook a large-scale work on generalised differential equations in functional derivatives.
His main books are Lecons d'analyse fonctionnelle (1922), Calcul des probabilités (1925), Théorie de l'addition des variables aléatoires (1937-54), and Processus stochastiques et mouvement brownien (1948).
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