Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T21:41:23.130Z Has data issue: false hasContentIssue false
  • English
  • Français

On a theorem of Zygmund

Published online by Cambridge University Press:  24 October 2008

M. Kac
M. Kac
Affiliation:
Cornell University, Ithaca, New York
Get access Rights & Permissions [Opens in a new window]

Extract

Zygmund (1) proved in 1936 that if f(x) ∈Lp(−∞, ∞) (1 ≤ p ≤ 2), the Fourier transform

exists for almost every λ, in the sense that

exists for almost every λ. The purpose of this note is to provide a short proof of this theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 3 , July 1951 , pp. 475 - 476
Copyright
Copyright © Cambridge Philosophical Society 1951

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

(1)Zygmund, A.A remark on Fourier transforms. Proc. Cambridge Phil. Soc. 32 (1936), 321–7.CrossRefGoogle Scholar
(2)Kac, M.Convergence and divergence of non-harmonic gap series. Duke Math. J. 8 (1941), 541–5.CrossRefGoogle Scholar
(3)Hartman, P.Divergence of non-harmonic gap series. Duke Math. J. 9 (1942), 404–5.CrossRefGoogle Scholar
(4)Menchoff, D.Sur les séries de fonctions orthogonales. Fund. Math. 11 (1928), 375–420, Theorem 12.Google Scholar