Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-26T19:41:04.447Z Has data issue: false hasContentIssue false
  • English
  • Français

Certain Fourier Transforms of Distributions

Published online by Cambridge University Press:  20 November 2018

Eugene Lukacs  and
Otto Szasz
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Fourier transforms of distribution functions are frequently studied in the theory of probability. In this connection they are called characteristic functions of probability distributions. It is often of interest to decide whether a given function φ(t) can be the characteristic function of a probability distribution, that is, whether it admits the representation

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 140 - 144
Copyright
Copyright © Canadian Mathematical Society 1951

References

[1] Bochner, S., Monotone Funktionen, Stieltjessche Intégrale und harmonische Analyse, Math. Ann., vol 108, (1933), 378–410.Google Scholar
[2] Cramer, H., On the representation of a function by certain Fourier integrals. Trans. Amer. Math. Soc, vol. 46, (1939), 191–201.Google Scholar
[3] Cramer, H., Mathematical methods of statistics (Princeton University Press, 1946).Google Scholar
[4] Khintchine, A., Zur Kennzeichnung der charakteristischen Funktionen. Bull. Math. Univ. Moscou, vol. 1 (1937), 1–31.Google Scholar
[5] Levy, P., L'arithmétique des lois de probabilités, J. Math. Pures Appliquées, vol. 17 (1938), 17–39.Google Scholar
[6] Marcinkiewicz, J., Sur une propriété de la loi de Gauss, Math. Zeit., vol. 44 (1938), 612–618.Google Scholar
[7] Pólya, G., Remarks on characteristic functions, Proceedings of the Berkeley Symposium on mathematical statistics and probability (1949), 115–123.Google Scholar
[8] Schoenberg, I. J., On totally positive functions, Laplace integrals and entire functions ef the Laguerre-Pólya-Schur type, Proc. Nat. Acad. Sci., vol. 33 (1947), 11–17.Google Scholar