Annali di Matematica Pura ed Applicata

, Volume 102, Issue 1, pp 177–202 | Cite as

Holomorphic almost periodic functions and positive-definite functions on Siegel domains

  • Edoardo Vesentini


Let D be a Siegel domain and let N be the nilpotent Lie group acting in a simply transitive way on the distinguished boundary of D. The existence of holomorphic almost periodic functions and of holomorphic positive-definite functions on D is investigated.


Periodic Function Distinguished Boundary Siegel Domain 
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  1. [1]
    L. Auslander -J. Brezin,Uniform distributions on Solvmanifolds, Advances in Mathematics,7 (1971), pp. 111–144.CrossRefMathSciNetGoogle Scholar
  2. [2]
    L. Auslander - L. Green - F. Hahn,Flows on homogeneous spaces, Annals of Mathematics Studies, no. 53, Princeton University Press, 1963.Google Scholar
  3. [3]
    S. Bochner - W. T. Martin,Several complex variables, Princeton University Press, 1948.Google Scholar
  4. [4]
    J. Dixmier, Sur les représentations unitaires des groupes de Lie nilpotents, II, Bull. Soc. Math. France,85 (1957), pp. 325–388.MATHMathSciNetGoogle Scholar
  5. [5]
    J. Dixmier, Sur les représentations unitaires des groupes de Lie nilpotents, III, Canad. J. Math.,10 (1958), pp. 321–348.MATHMathSciNetGoogle Scholar
  6. [6]
    J. Dixmier, Sur les représentations unitaires des groupes de Lie nilpotents, V, Bull. Soc. Math. France,87 (1957), pp. 65–79.MathSciNetGoogle Scholar
  7. [7]
    J. Dixmier,Les C* algèbres et leurs représentations, Gauthier-Villars, Paris, 1964.Google Scholar
  8. [8]
    S. Kaneyuki,Homogeneous bounded domains and Siegel domains, Lecture Notes in Mathematics,24 (1971), Springer-Verlag.Google Scholar
  9. [9]
    A. A. Kirillov,Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk,17 (1962), pp. 57–110.MATHMathSciNetGoogle Scholar
  10. [10]
    A. Koranyi,The Poisson integral for generalized half-planes and bounded symmetric domains, Ann. of Math.,82 (1965), pp. 332–350.CrossRefMATHMathSciNetGoogle Scholar
  11. [11]
    A. Koranyi -E. M. Stein,H 2 spaces of generalized half-planes, Studia Mathematica,43 (1972), pp. 379–388.MathSciNetGoogle Scholar
  12. [12]
    R. D. Odgen -S. Vàgi,Harmonic analysis and H 2-functions on Siegel domains of type II, Proc. Nat. Acad. Sci. USA,69 (1972), pp. 11–14.Google Scholar
  13. [13]
    L. Pukanszky,Leçons sur les représentations des groupes, Dunod, Paris, 1967.Google Scholar
  14. [14]
    I. I. Pyatetskii -Shapiro,Automorphic functions and the geometry of classical domains, Gordon and Breach, New York, 1969.Google Scholar
  15. [15]
    W. Rudin,Fourier analysis on groups, Interscience Publishers, New York, 1967.Google Scholar
  16. [16]
    S. Vagi,On the boundary values of holomorphic functions, Rev. Un. Mat. Argentina,25 (1970), pp. 123–136.MATHMathSciNetGoogle Scholar
  17. [17]
    E. Vesentini, Fonctions holomorphes presque-périodiques et fonctions de type positif sur les domaines de Siegel, C. R. Acad. Sc. Paris,274 (1972), pp. 1619–1622.MATHMathSciNetGoogle Scholar
  18. [18]
    A. Weil,L'intégration dans les groupes topologiques et ses applications, Hermann, Paris, 1965.Google Scholar
  19. [19]
    S. G. Gindikin,Analysis in homogeneous domains, Uspekhi Mat. Nauk,19 (1964), pp. 3–92.MATHMathSciNetGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1975

Authors and Affiliations

  • Edoardo Vesentini
    • 1
  1. 1.College Park

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