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On summation processes of Fourier expansions for spherical functions

Part of the Lecture Notes in Mathematics book series (LNM,volume 571)

Keywords

  • Symmetric Space
  • Banach Algebra
  • Spherical Function
  • Multiplier Theorem
  • Lebesgue Constant

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References

  1. Bonami, A., Clerc, J.L.: Sommes de Cesàro et multiplicateurs des développements en harmoniques sphériques. Trans. Amer. Math. Soc. 183, 223–263 (1973)

    MathSciNet  MATH  Google Scholar 

  2. Cartan, É: Sur la détermination d'un système orthogonal complet dans un espace de Riemann symétrique clos. Rend. Circ. Palermo 53, 217–253 (1929)

    CrossRef  MATH  Google Scholar 

  3. Clerc, J.L.: Les sommes partielles de la décomposition en harmoniques sphériques ne convergent pas dans Lp (p≠2). C. r. Acad. Sci., Paris, Sér A 274, 59–61 (1972)

    MathSciNet  MATH  Google Scholar 

  4. Clerc, J.L.: Sommes de Riesz et multiplicateurs sur un groupe de Lie compact. Ann. Inst. Fourier, Grenoble 24, 149–172 (1974)

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Coifman, R.R., Weiss, G.: Analyse harmonique non-commutative sur certains espaces homogènes. Lecture Notes in Mathematics, Vol. 242. Berlin-Heidelberg-New York 1971

    Google Scholar 

  6. Dieudonné, J.: Éléments d'Analyse. Tome VI. Gauthier-Villars Éditeur, Paris-Bruxelles-Montreal 1975

    MATH  Google Scholar 

  7. Dreseler, B.: Zu Entwicklungen nach sphärischen Funktionen gehörende Approximationsverfahren auf kompakten symmetrischen Mannigfaltigkeiten (to appear)

    Google Scholar 

  8. Dreseler, B. Lebesgue constants for spherical partial sums of Fourier series on compact Lie groups. In: Proceedings of the Colloquium on Fourier Analysis and Approximation Theory, Budapest 1976 (to appear)

    Google Scholar 

  9. Dreseler, B., Schempp, W.: On the convergence and divergence behaviour of approximation processes in homogeneous Banach spaces. Math. Z. 143, 81–89 (1975)

    CrossRef  MathSciNet  Google Scholar 

  10. Dunkl, C.F., Ramirez, R.E.: Topics in harmonic analysis. New York: Appleton-Century-Crofts 1971

    MATH  Google Scholar 

  11. Gelfand, I.M: Spherical functions on Riemannian symmetric spaces. Dokl. Akad. Nauk SSSR 70, 5–8 (1950)

    Google Scholar 

  12. Helgason, S.: Differential geometry and symmetric spaces. New York: Academic Press 1962

    MATH  Google Scholar 

  13. Hewitt, E., Ross, K.A.: Abstract harmonic analysis. Vol. II. Berlin-Heidelberg-New York: Springer-Verlag 1970

    MATH  Google Scholar 

  14. Hrach, R.: Über Summationsverfahren bei Fourier-Reihen auf der unitären Gruppe U(n). Diplomarbeit. Ruhr-Universität Bochum 1974.

    Google Scholar 

  15. Igari, S.: On multipliers of Hankel transforms. Tôhoku Math. J. (2) 24, 201–206 (1972)

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Stein, E.M.: Interpolation of linear operators. Trans. Amer. Math. Soc. 87, 159–172 (1958)

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton, New Jersey: Princeton University Press 1971

    MATH  Google Scholar 

  18. Varadarajan, V.S.: Lie groups, Lie algebras, and their representations. New York: Prentice Hall, INC. Englewood Cliffs, N.J. 1974

    MATH  Google Scholar 

  19. Warner, G.: Harmonic analysis on semi-simple Lie groups I. Berlin-Heidelberg-New York: Springer-Verlag 1972

    CrossRef  MATH  Google Scholar 

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© 1977 Springer-Verlag Berlin · Heidelberg

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Dreseler, B. (1977). On summation processes of Fourier expansions for spherical functions. In: Schempp, W., Zeller, K. (eds) Constructive Theory of Functions of Several Variables. Lecture Notes in Mathematics, vol 571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086565

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  • DOI: https://doi.org/10.1007/BFb0086565

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08069-5

  • Online ISBN: 978-3-540-37496-1

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