Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Arithmetic means of Fourier coefficients

Author: Rajendra Sinha
Journal: Proc. Amer. Math. Soc. 55 (1976), 83-86
MSC: Primary 42A16
Addendum: Proc. Amer. Math. Soc. 60 (1976), 243-244.
MathSciNet review: 0397274
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given the Fourier coefficients of an even continuous function, we find a necessary and sufficient condition such that their arithmetic means are the Fourier coefficients of an odd continuous function. A similar result is shown for those Lipschitz classes whose elements are automatically equivalent to continuous functions.

References [Enhancements On Off] (What's this?)

  • [1] R. Bellman, Note on a theorem of Hardy on Fourier constants, Bull. Amer. Math. Soc. 50(1944), 741-744. MR6, 125. MR 0011137 (6:125c)
  • [2] G. H. Hardy, Notes on some points in the integral calculus, Messenger Math. 58(1929), 50-52.
  • [3] G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals. I, Math. Z. 27(1928), 565-606. MR 1544927
  • [4] -, A convergence criterion for Fourier series, Math. Z. 28(1928), 612-634. MR 1544980
  • [5] M. Kinukawa and S. Igari, Transformations of conjugate functions, Tôhoku Math. J. (2) 13(1961), 274-280. MR26 #2829. MR 0145298 (26:2829)
  • [6] A. A. Konyuškov, On Lipschitz classes, Izv. Akad. Nauk SSSR Ser. Mat. 21(1957), 423-448. (Russian) MR19, 546. MR 0088601 (19:546c)
  • [7] E. S. Quade, Trigonometric approximation in the mean, Duke Math. J. 3(1937), 529-543. MR 1546008
  • [8] Rajendra Sinha, On an infinite linear combination of partial sums of Fourier series, Studia Math. (to appear). MR 0425482 (54:13437)
  • [9] A. Zygmund, Trigonometric series. Vols. I, II, 2nd ed., Cambridge Univ. Press, New York and London, 1968. MR38 #4882. MR 0236587 (38:4882)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A16

Retrieve articles in all journals with MSC: 42A16

Additional Information

Keywords: Fourier series, conjugate function, Lipschitz class, strong summability, closed graph theorem
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society