Notes on Fourier series (V): Summability (R1)

Abstract

1·1. There is a familiar method of summation of series usually called the method (R, 1), or sometimes Lebesgue's method. If sn = u0 + u1 + … + un and, as it will be convenient to suppose throughout, u0 = 0, thenwhen h → + 0§ the convergence of the series for small positive h is presupposed. The method is not 'regular'; there are convergent series not summable (R, 1).