Some new convergence criteria for Fourier series

Godfrey Harold Hardy; John Edensor Littlewood

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1934)

  • Volume: 3, Issue: 1, page 43-62
  • ISSN: 0391-173X

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Hardy, Godfrey Harold, and Littlewood, John Edensor. "Some new convergence criteria for Fourier series." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.1 (1934): 43-62. <http://eudml.org/doc/82870>.

@article{Hardy1934,
author = {Hardy, Godfrey Harold, Littlewood, John Edensor},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {series},
language = {eng},
number = {1},
pages = {43-62},
publisher = {Scuola normale superiore},
title = {Some new convergence criteria for Fourier series},
url = {http://eudml.org/doc/82870},
volume = {3},
year = {1934},
}

TY - JOUR
AU - Hardy, Godfrey Harold
AU - Littlewood, John Edensor
TI - Some new convergence criteria for Fourier series
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1934
PB - Scuola normale superiore
VL - 3
IS - 1
SP - 43
EP - 62
LA - eng
KW - series
UR - http://eudml.org/doc/82870
ER -

References

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  1. 1 G.H. Hardy and J.E. Littlewood: Theorems concerning the summability of series by Borel's exponential method. Rendiconti di Palermo, 41 (1916), 36-53. Zbl46.0486.04JFM46.0486.04
  2. 2 - - Notes on the theory of series (IV): The strong summabitity of Fourier series. Proc. London Math. Soc. (2), 26 (1927), 273-286. 
  3. 3 - - Notes on the theory of series (VII): On Young's convergence criterion for Fourier series. Proc. London Math. Soc. (2), 28 (1928), 301-311. Zbl54.0302.01
  4. 4-5 - - Some properties of fractional integrals. Math. Zeitschrift, 28 (1928), 565-606 and 34 (1931), 403-439. Zbl54.0275.05
  5. 6 - - Notes on the theory of series (XVII): Some new convergence criteria for Fourier series. Journal London Math. Soc., 7 (1932), 252-256. Zbl0005.39402
  6. 7 E.W. Hobson: The theory of functions of a real variable. Vol. 2, ed. 2, Cambridge, 1926. 
  7. 8 S. Pollard: On the criteria for the convergence of a Fourier series. Journal London Math. Soc., 2 (1927), 255-262. Zbl53.0252.01JFM53.0252.01
  8. 9 R. Schmidt: Über das Borelsche Summierungsverfahren. Schriften der Königsberger gelehrten Gesellschaft, 1 (1925), 202-256. JFM51.0184.01
  9. 10 G. Valiron: Remargues sur la sommation des séries divergentes par les méthodes de M. Borel. Rendiconti di Palermo, 42 (1917), 267-284. Zbl46.0487.01JFM46.0487.01
  10. 11 T. Vijayaraghavan: A theorem concerning the summability of series by Borel's method. Proc. London Math. Soc. (2), 27 (1928), 316-326. Zbl54.0237.01JFM54.0237.01
  11. 12 N. Wiener: Tauberian theorems. Annals of Mathematics, 33 (1932), 1-100. Zbl0004.05905JFM58.0226.02
  12. 13 — The Fourier integral and certain of its applications. Cambridge, 1933. 

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