Bochner and Schoenberg theorems on symmetric spaces in the complex case

Piotr Graczyk; Jean-Jacques Lœb

Bulletin de la Société Mathématique de France (1994)

  • Volume: 122, Issue: 4, page 571-590
  • ISSN: 0037-9484

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Graczyk, Piotr, and Lœb, Jean-Jacques. "Bochner and Schoenberg theorems on symmetric spaces in the complex case." Bulletin de la Société Mathématique de France 122.4 (1994): 571-590. <http://eudml.org/doc/87705>.

@article{Graczyk1994,
author = {Graczyk, Piotr, Lœb, Jean-Jacques},
journal = {Bulletin de la Société Mathématique de France},
keywords = {spherical Fourier transform; positive definite functions; Bochner theorem; Schoenberg theorem; Levy-Khinchine formulae},
language = {eng},
number = {4},
pages = {571-590},
publisher = {Société mathématique de France},
title = {Bochner and Schoenberg theorems on symmetric spaces in the complex case},
url = {http://eudml.org/doc/87705},
volume = {122},
year = {1994},
}

TY - JOUR
AU - Graczyk, Piotr
AU - Lœb, Jean-Jacques
TI - Bochner and Schoenberg theorems on symmetric spaces in the complex case
JO - Bulletin de la Société Mathématique de France
PY - 1994
PB - Société mathématique de France
VL - 122
IS - 4
SP - 571
EP - 590
LA - eng
KW - spherical Fourier transform; positive definite functions; Bochner theorem; Schoenberg theorem; Levy-Khinchine formulae
UR - http://eudml.org/doc/87705
ER -

References

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  2. [2] DENY (J.). — Notions sur les semigroupes d'opérateurs linéaires, cours rédigé par J. Faraut, Faculté des Sciences d'Orsay, Département de Mathématiques, 1963. 
  3. [3] FELLER (W.). — An Introduction to Probability Theory, vol. 2. — Wiley, New York, 1966. Zbl0138.10207
  4. [4] FLENSTED-JENSEN (M.). — Spherical functions on a real semisimple Lie group. A method of reduction to the complex case, J. Funct. Anal., t. 30, 1978, p. 106-146. Zbl0419.22019MR80f:43022
  5. [5] GANGOLLI (R.). — Isotropic infinitely divisible measures on symmetric spaces, Acta Math., t. 111, 1964, p. 213-246. Zbl0154.43804MR28 #4557
  6. [6] GETOOR (R.K.). — Infinitely divisible probabilities on the hyperbolic plane, Pacific J. Math., t. 11, 1961, p. 1287-1308. Zbl0124.34502MR24 #A3682
  7. [7] GRACZYK (P.). — A central limit theorem on the space of positive definite symmetric matrices, Ann. Inst. Fourier, t. 42, 1992, p. 857-874. Zbl0736.60025MR93m:60023
  8. [8] GRACZYK (P.). — Dispersions and a central limit theorem on symmetric spaces, to appear in Bull. Sci. Math. Zbl0829.43002
  9. [9] GRACZYK (P.). — Cramér theorem on symmetric spaces of noncompact type, to appear in J. Theor. Prob. Zbl0808.60013
  10. [10] HELGASON (S.). — Analysis on Lie Groups and Homogeneous Spaces, Regional Conference Series in Mathematics, 14, AMS, Providence R.I., 1972. Zbl0264.22010MR47 #5179
  11. [11] HELGASON (S.). — Groups and Geometric Analysis. — Academic Press, New York, 1984. Zbl0543.58001MR86c:22017
  12. [12] LUKACS (E.). — Characteristic Functions. — Griffin, London, 1960. Zbl0087.33605MR23 #A1392
  13. [13] RICHARDS (D.St.P.). — The central limit theorem on spaces of positive definite matrices, J. Multivariate Anal., t. 29, 1989, p. 326-332. Zbl0681.60026MR91a:60031
  14. [14] TERRAS (A.). — Harmonic Analysis on Symmetric Spaces and Applications II. — Springer Verlag, New York, 1988. Zbl0668.10033MR89k:22017

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