FEJÉR, LÉOPOLD - THE "FUNDAMENTAL SUMMATION THEOREM" DISCOVERED.

Sur les fonctions bornées et intégrables.

(Paris, Gauthier-Villars), 1900. 4to. No wrappers. In: "Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences", Tome 131, No 24. Pp. (975-) 1017. (Entire issue offered). Fejér's (here spelled Téjer !) paper: pp. 984-987. Clean and fine.

First printing of this importent paper in which Féjer states the "Summation Theorem" that bears his name.
"Fejér’s main works deal with harmonic analysis. His classic theorem on (C, 1) summability of trigonometric Fourier series (1900) not only gave a new direction to the theory of orthogonal expansions but also, through significant applications, became a starting point for the modern general theory of divergent series and singular integrals. Through a Tauberian theorem of G. H. Hardy’s the convergence theory of Fourier series was considerably affected by Fejér’s theorem as well; it is closely connected with Weierstrass’ approximation theorems and with the more advanced theory of power series and harmonics (potential theory), and makes possible a number of analogues for related series, such as Laplace series."(DSB).

Order-nr.: 51494