The “Fourier” Theory of the Cardinal Function
- 1 July 1928
- journal article
- Published by Cambridge University Press (CUP) in Proceedings of the Edinburgh Mathematical Society
- Vol. 1 (3) , 169-176
- https://doi.org/10.1017/s0013091500013511
Abstract
The generalised Riesz-Fischer theorem states that if is convergent, with 1 < p ≤ 2, then is the Fourier series of a function of class . When p > 2 the series (2) is not necessarily a Fourier series; neither is it necessarily a Fourier D-series. It will be shown below that it must however be what may be called a “Fourier Stieltjes” series. That is to say, the condition (1) with (p > 1) implies that there is a continuous function F (x) such thatThis publication has 2 references indexed in Scilit:
- A case of distinction between Fourier integrals and Fourier seriesMathematical Proceedings of the Cambridge Philosophical Society, 1927
- The Summation of a Fourier Integral of Finite TypeMathematical Proceedings of the Cambridge Philosophical Society, 1926