The Parseval formulae for monotonic functions. III
Sheila M. Edmonds · Mathematical Proceedings of the Cambridge Philosophical Society · 1950
This sequence of papers is concerned with a group of theorems on Fourier transforms, and with the corresponding results for Fourier series. The transform theorems deal with the equations when two of the functions concerned are monotonic; and the series theorems, with the equations when two of the functions or sequences of coefficients are monotonic. A general survey of the problem was given in two earlier papers, which we shall call M.F. (I) and M.F. (II), and the results obtained were tabulated in M.F. (II). There is thus no need to restate the position in detail here. We shall merely recall as briefly as possible what has been proved already, so as to show the scope of the present paper.