Skip to main content
Log in

Multivariate versions and two problems of Schoenberg

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature cited

  1. M. L. Eaton, “On the projections of isotropic distributions,”Ann. Stat,9, No. 2, 391–400 (1981).

    Google Scholar 

  2. I. J. Schoenberg, “Metric spaces and positive-definite functions,”Trans. Amer. Math. Soc.,44, No. 3, 522–536 (1938).

    Google Scholar 

  3. J. K. Misiewicz, “Positive-definite norm-dependent functions onl t8,” Preprint, Delft University of Technology, 1–11 (1988).

  4. J. Bretagnolle, D. Dacuncho-Castelle, and J. L. Krivine, “Lois stables et espacesL p,”Ann. Inst. H. Poincaré, Sec. B,11, No. 3, 231–259 (1966).

    Google Scholar 

  5. Yu. G. Kuritsyn and A. V. Shestakov, “On α-symmetric distributions,”Teor. Veroyatn. i Prim.,29, No. 4, 769–772 (1984).

    Google Scholar 

  6. J. K. Misiewicz and C. L. Scheffer, “Pseudo-isotropic measures,”Rpts. Fac. Techn. Math. Inform., Delft University of Technology No. 88–33, 1–39 (1988).

    Google Scholar 

  7. I. A. Katasonov and Yu. G. Kuritsyn, “On a property of then-dimensional version of a distribution law,” Manuscript deposited with VINITI, Moscow (1985).

  8. D. Kelker, “Distribution theory of spherical distributions and a location-scale parameter generalization,”Sankhya, Ser. A,32, 419–430 (1970).

    Google Scholar 

  9. S. T. Huahg and S. Cambanis, “Spherically invariant processes: Theory of nonlinear structure, discrimination, and estimation,”J. Multiv. Anal.,9, No. 1, 59–83 (1979).

    Google Scholar 

  10. W. Linde, “Extensions of the Slepian lemma top-stable measures,”Lect. Notes Math., No. 1080, 162–169 (1984).

    Google Scholar 

  11. G. H. Hardy, J. E. Littlewood and G. Pólya,Inequalities, 2nd ed., Cambridge University Press, New York (1952).

    Google Scholar 

  12. V. M. Zolotarev,One-dimensional Stable Distributions, American Mathematical Society, Providence (1986).

    Google Scholar 

  13. S. Cambanis, R. Keener, and G. Simons, “Onα-symmetric multivariate distributions,”Inst. Stat. Mimeo. Ser., No. 1350, 1–30 (1981).

    Google Scholar 

  14. D. S. Richards, “Positive-definite symmetric functions on finite-dimensional spaces. I. Applications of the Radon transform,”J. Multiv. Anal.,19, No. 2, 280–298 (1986).

    Google Scholar 

  15. Yu. G. Kuritsyn, “On systems of spherically symmetric random variables,”Tr. Mat. Fak. Voronezh, No. 6, 52–58 (1972).

    Google Scholar 

  16. J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces. II: Function Spaces, Springer, Berlin (1979).

    Google Scholar 

  17. I. J. Schoenberg, “Metric spaces and completely monotone functions,”Ann. Math.,39, No. 4, 811–841.

  18. C. S. Hertz, “A class of negative-definite functions,”Proc. Amer. Math. Soc.,14, 670–676.

Download references

Authors

Additional information

Translated from:Problemy Ustoichivosti Stokhasticheskikh Modelei, Trudy Seminara, 1989, pp. 72–79.

The author wishes to thank Jolantha Misiewicz for allowing the use of her works [3] and [6].

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuritsyn, Y.G. Multivariate versions and two problems of Schoenberg. J Math Sci 59, 939–945 (1992). https://doi.org/10.1007/BF01099122

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01099122

Keywords

Navigation