Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-23T10:48:47.705Z Has data issue: false hasContentIssue false
  • English
  • Français

On some series of functions, (1)

Published online by Cambridge University Press:  24 October 2008

R. E. A. C. Paley  and
A. Zygmund
R. E. A. C. Paley
Affiliation:
Trinity College
Get access Rights & Permissions [Opens in a new window]

Extract

Let c0, c1,…, cn,…be a sequence of real constants, and ƒ0(x), ƒ1(x),…, ƒn(x),… a sequence of functions defined, for example, in the interval (0, 1). In this paper we shall investigate some of the properties of the series

which may be obtained from the standard series

by interchanging the signs of the terms in a quite arbitrary way.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 26 , Issue 3 , July 1930 , pp. 337 - 357
Copyright
Copyright © Cambridge Philosophical Society 1930

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Hardy, G. H. and Littlewood, J. E., 1; “A maximal theorem with function-theoretic applications,“ Acta Math. LIV (1930), 81–116.Google Scholar
Khintchine, A. and Kolmogoroff, A., 1; “Über Konvergenz von Reihen, deren Glieder durch den Zufall bestimmt werden,” Recueil de la Soc. Math. de Moscou, XXXII (1925), 668–677.Google Scholar
Kolmogoroff, A. and Seliverstoff, G., 1; “Sur la convergence de séries de Fourier,” Comptes Rendus, CLXXVIII (1924), 303–306.Google Scholar
Littlewood, J. E., 1; “On the mean values of power series,” Proc. London Math. Soc. (2), XXV (1926), 328–337.CrossRefGoogle Scholar
Paley, R. E. A. C., 1; “On some problems connected with Weierstrass's non-differentiable function,” Proc. London Math. Soc., to be published.Google Scholar
Rademacher, H., 1; “Einige Sätze über Reihen von allgemeinen Orthogonal-funktionen,” Math. Annalen, LXXXVII (1922), 112–138.Google Scholar
Sidon, S., 1; “Verallgemeinerung eines Satzes über die absolute Konvergenz von Fourierreihen mit Lücken,” Math. Annalen, XCVII (1927), 675–676.CrossRefGoogle Scholar
Steinhaus, H., 1; “Über die Wahrscheinlichkeit dafür, daß der Konvergenzkreis einer Potenzreihe ihre natürliche Grenze ist,” Math. Zeitschrift, XXI (1929), 408–416.Google Scholar
Töoplitz, O., 1; “Über allgemeinelineare Mittelbildungen,” Prace Matematyczno-Fizyczne, XXII (1911), 113–119.Google Scholar
Young, W. H., 1; “On classes of summable functions and their Fourier series,” Proc. Royal Soc. (A), LXXXVII (1912), 225–229.Google Scholar
Zygmund, A., 1; “Sur les séries trigonométriques lacunaires,” Journal London Math. Soc. V (1930), 138–145.CrossRefGoogle Scholar
Zygmund, A., 2; “On the convergence of lacunary trigonometric series,” Fundamenta Math. XVI (1930), to be published.Google Scholar