Théorie générale des fonctionnelles:

Abstract

IN the modern mathematical development of operational methods, the theory of integral equations has yielded a calculus of so broad a generality that it has very considerably extended the field of analysis. The foundations of the theory were laid almost simultaneously by E. I. Fredholm of Stockholm and Vito Volterra of Rome, whose brilliant papers opened to the mathematical world one of its most fertile regions. The first treatises on the subject were two monographs written by Prof. Volterra and published in Paris in 1913. They were entitled, “Leçons sur les fonctions de lignes”and “Leçons sur les équations intégrales et les équations intégro-différentielles”, and were based upon courses of lectures given by the author at the Sorjbonne and at Rome respectively. In 1936, a new edition of the latter book became necessary and, in view of the rapid progress made in the theory since 1913, the author in collaboration with Prof. Pérés, of Paris, decided to rewrite the work under the new title, “Théorie générate des fonctionnelles”, of which the book under review is the first of three volumes.

Théorie générale des fonctionnelles:

(Collection de monographies sur la théorie des fonctions.) Tome 1: Généralités sur les fonctionnelles ; Théorie des équations intégrales. Par Prof. Vito Volterra and Prof. Joseph Pèrés. Pp. xii+359. (Paris: Gauthier-Villars, 1936.) 100 francs.