ALMOST PERIODIC FUNCTIONS

BOHR, HARALD.

Zur Theorie der Fast Periodischen Funktionen. I-III. (I. Eine Verallgemeinerung der Theorie der Fourierreihen - II. Zusammenhang der fastperiodischen Funktionen mit Funktionen von unendlich vielen Variabeln; gleichmässige Approximation durch trigonometrische Summen.- III. Dirichletentwicklung analytischer Funktionen).

(Berlin, Stockholm, 1924-25). 4to. Bound in one full fabrikoid. As issued in "Acta Mathematica", vols 45,46,47. - Pp. 29-127, pp. 102-214 - pp. 238-281. Clean and fine. A very small tear to the last two leaves repaired without loss.

First edition of Harald Bohr's main work. Harald Bohr was younger brother to Niels Bohr. "The problem of which function may be represented by Dirichlet series led Bohr to his main achievement, the theory of almost periodic functions, on which the greater part of his later work is concentrated....Whereas hitherto in the theory of Dirichlet series one always worked withh frequencies forming a monotonic sequence, Bohr discovered that in order to obtain an answer to the problem one would have to consider series with quite arbitrary frequencies. The answer was obtained by introducing the notion of almost periocicity. The theory was published in three papers (the offered papers) in "Acta Mathematica", and numerous mathematicians joined in the work on its simplification and extension. Thus Weil and Wiener connected it with the classical theories of integral equations and Fourier integrals, and Bochner developed a summation method for Bohr-Fourier series gneralizing Fejér's theorem." (Børge Jessen in DSB).

Order-nr.: 38967