The Parseval formulae for monotonic functions. III-Reference-Cited by-同舟云学术

The Parseval formulae for monotonic functions. III

Published:1950-04 Issue:2 Volume:46 Page:249-267
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

Edmonds Sheila M.

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference7 articles.

1. ‘The Pareeval formulae for monotonic functions. I’, Proc. Cambridge Phil. Soc. 43 (1947), 289–306

2. ‘On the Parseval formulae for Fourier transforms’, Proc. Cambridge Phil. Soc. 38 (1942), 1–19.

3. ‘The Parseval formulae for monotonic functions. II’, Proc. Cambridge Phil. Soc. 46 (1950), 231–248.

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Some further asymptotic properties of Fourier constants;Mathematische Zeitschrift;1958-12

2. Über trigonometrische Reihen mit monoton fallenden Koeffizienten;Archiv der Mathematik;1958-04

3. The Parseval formulae for monotonic functions. IV;Mathematical Proceedings of the Cambridge Philosophical Society;1953-04

4. The Parseval formulae for monotonic functions. II;Mathematical Proceedings of the Cambridge Philosophical Society;1950-04