Notes on Fourier series (V): Summability (R1)
Published online by Cambridge University Press: 24 October 2008
Extract
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, then
when 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).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 2 , April 1949 , pp. 173 - 185
- Copyright
- Copyright © Cambridge Philosophical Society 1949
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