Spherical distributions: Schoenberg (1938) revisited

Expositiones Mathematicae

Volumn 23, Issue 3, 2005, Pages 281-287

  Steerneman, A G M ^a   van Perlo ten Kleij, F ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

Characteristic function; Normal distribution; Spherical distribution

Indexed keywords

EID: 24344492281     PISSN: 07230869     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.exmath.2005.01.002     Document Type: Article

References (11)

1. R.B. Ash, Real Analysis and Probability, Academic Press, New York, 1972.
2. C. Berg, J.P.R. Christensen, P. Ressel, Harmonic Analysis on Semigroups. Theory of Positive Definite and Related Functions, Graduate Texts in Mathematics, vol. 100, Springer, Berlin, Heidelberg, New York.
3. P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968.
4. S. Cambanis, S. Huang, G. Simons, On the theory of elliptically contoured distributions, J. Multivariate Anal. 11 (1981) 368-385.
5. W.F. Donoghue Jr., Distributions and Fourier Transforms, Academic Press, New York, 1969.
6. M.L. Eaton, A characterization of spherical distributions, J. Multivariate Anal. 20 (1986) 272-276.
7. K.T. Fang, S. Kotz, K.W. Ng, Symmetric Multivariate and Related Distributions, Chapman & Hall, London, 1990.
8. P.H. Hartman, A. Wintner, On the spherical approach to the normal distribution law, Amer. J. Math. 62 (1940) 759-779.
9. J.F.C. Kingman, On random sequences with spherical symmetry, Biometrika 59 (1972) 492-494.
10. C. Müller, Spherical Harmonics, Lecture Notes in Mathematics, vol. 17, Springer, Berlin, Heidelberg, New York, 1966.
11. I.J. Schoenberg, Metric spaces and completely monotone functions, Ann. Math. 39 (4) (1938) 811-841.