POINCARÉ, H.

Remarques diverses sur l'équation de Fredholm.

[Berlin, Stockholm, Paris, Beijer, 1910] 4to. Without wrappers as extracted from "Acta Mathematica. Hrdg. von G. Mittag-Leffler.", Bd. 33, pp. 57-86.

First printing of Poincaé's work on Fredholm's equation.
"... heuristic variational arguments convinced Poincaré that there should be a sequence of "eigenvalues" and corresponding "eigenfunctions" for this problem, but for the same reasons lit was not able to prove their existence. A few years later, Fredholm's theory of integral equations enabled him to solve all these problems; it is likely that Poincareé's papers had a decisive influence on the development of Fredholm's method, in particular the idea of introducing a variable complex parameter in the integral equation. It should also be mentioned that Fredholm's determinants were directly inspired by the theory of "infinite determinants" of H. von Koch, which itself was a development of much earlier results of Poincaré in connection with the solution of linear differential equations." (DSB)

Order-nr.: 45841