HADAMARD, JACQUES.

Theorie des équations aux dérivées partielles linéaires hyperboliques et du probléme de Cauchy.

(Berlin, Stockholm, Paris, Almqvist & Wiksell, 1907). 4to. Without wrappers as extracted from "Acta Mathematica. Hrsg. von G. Mittag-Leffler", Bd. 31, pp. 333-380.

First printing of Hadamard's paper on Cauchy's problem in linear differential equations.

"Hadamard fully set out the idea of the correctly posed problem for equations with partial derivatives in his excellent Lectures on Cauchy's Problem in Linear Differential Equations (1922; French ed., 1932). Thus, for Laplace's equation, Dirichlet's problem is a correctly posed problem; on the other hand, for an equation of the hyperbolic type, Cauchy's problem is the one which meets this criterion. These ideas have had a great influence on modern research because they have shown the necessity of introducing different types of neighborhoods and, in consequence, different species of continuity; these conceptions led to general topology and functional analysis. Also in the Lectures is the notion of the "elementary solution" which has so much in common with that of "distribution" (or "generalized function"). Also in connection with equations with partial derivatives, one should mention the concept of the "finite portion" of a divergent integral, which plays an essential role in the solution of Cauchy's problem." (DSB)

Order-nr.: 50400