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Infinitely divisible probaility measures on compact groups

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Lectures on Operator Algebras

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 247))

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References

  1. S. Bochner: Harmonic Analysis and the Theory of Probability, University of California Press (1960)

    Google Scholar 

  2. S. Bochner: Positive zonal functions on spheres Proc. Nat. Acad. Sci. 40 (1954), 1141–1147.

    Article  MathSciNet  MATH  Google Scholar 

  3. W. Böge: Über die Charakterisierung unendlich oft teilbarer Wahrscheinlichkeitsverteilungen J. reine und angew. Math. 201 (1959), 150–156.

    MATH  Google Scholar 

  4. W. Böge: Zur Charakterisierung sukzessiv unendlich teilbarer Wahrscheinlichkeitsverteilungen auf lokalkompakten Gruppen. Z. Wahrscheinlichkeitstheorie und ver. Geb. 2 (1963/64), 380–394.

    Article  MathSciNet  MATH  Google Scholar 

  5. N. Bourbaki: Eléments de Mathématique: Livre VI Intégration, chapitres 1–4 (1965), chapitres 7–8 (1963), chapitre IX (1969)

    Google Scholar 

  6. H. Carnal: Unendlich teilbare Wahrscheinlichkeitsverteilungen auf kompakten Gruppen Math. Ann. 153 (1964), 351–383.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Carnal: Deux théorèmes sur les groupes stochastiques compacts. Comm. Math. Helv. 40 (1966), 237–246.

    Article  MathSciNet  MATH  Google Scholar 

  8. H. Carnal: Systèmes infinitésimaux sur les groupes topologiques compacts. Colloque International du CNRS sur les Probabilités sur les Structures Algébriques à Clermont-Ferrand (1970), 43–49.

    Google Scholar 

  9. C. Chevalley: Theory of Lie groups I. Princeton University Press (1946)

    Google Scholar 

  10. G. Choquet: Lectures on Analysis I. W. A. Benjamin, Inc. (1969)

    Google Scholar 

  11. Ph. Courrège: Générateur infinitésimal d'un semigroupe de convolution sur Rn et formule de Lévy-Khinchine. Bull. Sc. Math. 2esérie, 88 (1964), 3–30.

    MATH  Google Scholar 

  12. R. Gangolli: Isotropic infinitely divisible measures on symmetric spaces. Acta Math. 111 (1964), 213–246.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. A. Goldstein: Semigroups of Operators and Abstract Cauchy Problem. Lecture Notes: Department of Mathematics, Tulane University (1970).

    MATH  Google Scholar 

  14. U. Grenander: Probabilities on Algebraic Structures Almquist and Wiksell (1963).

    Google Scholar 

  15. Harish-Chandra: Lie algebras and the Tannaka duality theorem. Ann. of Math., 51 (1950), 299–330.

    Article  MathSciNet  MATH  Google Scholar 

  16. W. Hazod, L. Schmetterer: Über Poissongesetze auf lokalkompakten Gruppen und verwandte Fragen. Studia Sc. Math. Hung. 5 (1970), 63–74.

    MathSciNet  MATH  Google Scholar 

  17. S. Helgason: Differential Geometry and Symmetric Spaces. Academic Press (1962).

    Google Scholar 

  18. E. Hewitt, K. A. Ross: Abstract Harmonic Analysis I, II Springer (1963/1970).

    Google Scholar 

  19. H. Heyer: Über Haarsche Maße auf lokalkompakten Gruppen. Arch. Math. XVII (1966), 347–351.

    Article  MathSciNet  MATH  Google Scholar 

  20. H. Heyer: Fourier transforms and probabilities on locally compact groups. Jahresbericht d. DMV 70 (1968), 109–147.

    MathSciNet  MATH  Google Scholar 

  21. H. Heyer: L'analyse de Fourier non-commutative et applications à la théorie des probabilités. Ann. Inst. H. Poincaré IV (1968), 143–164.

    MathSciNet  MATH  Google Scholar 

  22. E. Hlawka: Statistik auf kompakten Gruppen. Österr. Akad. Wiss. Math.-Naturwiss. Klasse Anzeiger 4 (1959), 64–76.

    MATH  Google Scholar 

  23. K. H. Hofmann: Oral communication (1971).

    Google Scholar 

  24. G. A. Hunt: Semigroups of measures on Lie groups. TAMS 81 (1956), 269–293.

    Google Scholar 

  25. N. Jacobson: Lie algebras. Interscience (1962)

    Google Scholar 

  26. B. M. Kloss: Limiting distributions on bicompact abelian groups. Theory of Probability and its Application VI (1961), 361–389.

    Article  MathSciNet  MATH  Google Scholar 

  27. B. M. Kloss: Stable distributions on a class of locally compact groups. Theory of Probability and its Application VII (1962), 237–257.

    Article  MathSciNet  MATH  Google Scholar 

  28. K. McKennon: Multipliers, positive functionals, positive definite functions and Fourier-Stieltjes transforms. Memoir of the AMS 111 (1971).

    Google Scholar 

  29. P. A. Meyer: Probability and Potentials Blaisdell Publ. Co. (1966).

    Google Scholar 

  30. K. R. Parthasarathy: The central limit theorem for the rotation group. Theory of Prob. and its Appl. IX (1964), 248–257.

    Article  Google Scholar 

  31. K. R. Parthasarathy: On the embedding of an infinitely divisible distribution in a one-parameter convolution semigroup. Theory of Prob. and its Appl. XII (1967), 373–380.

    Article  Google Scholar 

  32. K. R. Parthasarathy: Probability Measures on Metric Spaces. Academic Press (1967).

    Google Scholar 

  33. K. R. Parthasarathy, R. Ranga Rao, S.R.S. Varadhan: Probability distributions on locally compact abelian groups. Illinois J. Math. 7 (1963), 337–369.

    MathSciNet  MATH  Google Scholar 

  34. K. R. Parthasarathy, V. V. Sazonov: On the representation of infinitely divisible distributions on locally compact abelian groups. Theory of Prob. and its Appl. IX (1964), 118–122.

    MathSciNet  MATH  Google Scholar 

  35. L. Schmetterer: Sur les lois de Poisson. Colloque International du CNRS sur les Probabilités sur les Structures Algébriques à Clermont-Ferrand (1970), 311–318.

    Google Scholar 

  36. L. Schmetterer: Poisson laws on groups. Proceedings of the 6th Berkeley Symposium. Math Statist. Probability (forthcoming).

    Google Scholar 

  37. Séminaire Sophus Lie: Théorie des Algèbres de Lie, Topologie des Groupes de Lie. 1 e année (1954/1955). Secrétariat Mathématique, 11 rue Pierre Curie, Paris 5e (1955).

    Google Scholar 

  38. E. M. Stein: Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. Annals of Mathematics Studies 63 (1970).

    Google Scholar 

  39. V. N. Tutubalin: Asymptotic behavior of convolutions of measures in the Lobachevskian plane and space. Theory of Prob. and its Appl. VII (1962), 189–196.

    Article  Google Scholar 

  40. K. Urbanik: Poisson distributions on compact abelian topological groups. Coll. Math. VI (1958), 13–24.

    MathSciNet  MATH  Google Scholar 

  41. K. Urbanik: Gaussian measures on locally compact abelian topological groups. Studia Math. XIX (1960), 77–88.

    MathSciNet  MATH  Google Scholar 

  42. N. N. Vorobev: The addition of independent random variables on finite groups. Mat. Sbornik 34 (1954), 89–126.

    MathSciNet  Google Scholar 

  43. D. F. Wehn: Probabilities on Lie groups. Proc. Nat. Acad. Sc. 48 (1962), 791–795.

    Article  MathSciNet  MATH  Google Scholar 

  44. A. Weil: Intégration dans les Groupes Topologiques et ses Applications. Hermann et Cie (1953).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Tübingen, Tübingen, Germany

    Herbert Heyer

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  1. Herbert Heyer
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© 1972 Springer-Verlag

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Heyer, H. (1972). Infinitely divisible probaility measures on compact groups. In: Lectures on Operator Algebras. Lecture Notes in Mathematics, vol 247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058552

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  • DOI: https://doi.org/10.1007/BFb0058552

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05729-1

  • Online ISBN: 978-3-540-37117-5

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