A Property of Indefinitely Differentiable Classes

VOL. 18, 1932

MA THEMA TICS: W. J. TRJITZINSK7Y

719

4 W. J. Trjitzinsky, "Analytic Theory of Linear g-Difference Equations," hereafter referred to as (T). This paper will appear in the Acta Mathematica. ' For W(u), W'(l), W' more general subregions of W(u), WQ), W, respectively, can be taken (cf. (T; § 2)). 6 Concerning iterations cf. G. D. Birkhoff, "General Theory of Linear Difference Equations," Trans. Am. Math. Soc., 12, 243-284 (1911) and Birkhoff and Trjitzinsky, "Analytic Theory of Singular Difference Equations," Acta Mathematca, 60, 1-2, 1-89 (1932). The latter paper will be refefred to as (BT).

A PROPERTY OF INDEFINITELY DIFFERENTIABLE CLASSES BY W. J. TRJITZINSKY DEPARTMENT OF MATHEMATICS, NORTHWESTERN UxIvERsrrY Communicated November 15, 1932

A convenient way of defining classes of functions f(x), indefinitely differentiable on an interval (a, b) [a < b], is by letting CA denote the class of functions such that | < fvAv (V = O, 1..; a <x