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ArticleOriginal scientific text

Title

Invariant operators on function spaces on homogeneous trees

Authors 1, 2, 3

Affiliations

  1. School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia
  2. Dipartimento di Statistica, Università 'Bicocca', Edificio U7, II piano, viale Sarca 202, I-20100 Milano, Italy
  3. Facoltà di Scienze, Università dell'Insubria-Polo di Como, via Lucini 3, I-22100 Como, Italy

Keywords

ENG
spherical functions, harmonic analysis, homogeneous trees

Bibliography

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  2. [CS] J.-L. Clerc and E. M. Stein, Lp multipliers for noncompact symmetric spaces, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 3911-3912.
  3. [CGM] M. Cowling, S. Giulini and S. Meda, Lp-Lq estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. I, Duke Math. J. 72 (1993), 109-150.
  4. M. Cowling, S. Meda and A. G. Setti, Estimates for functions of the Laplace operator on homogeneous trees, Trans. Amer. Math. Soc., to appear.
  5. M. Cowling, S. Meda and A. G. Setti, An overview of harmonic analysis on the group of isometries of a homogeneous tree, Exposition. Math. 16 (1998), 385-423.
  6. [FTN] A. Figà-Talamanca and C. Nebbia, Harmonic Analysis and Representa- tion Theory for Groups Acting on Homogeneous Trees, London Math. Soc. Lecture Note Ser. 162, Cambridge Univ. Press, Cambridge, 1991.
  7. [FTP] A. Figà-Talamanca and M. Picardello, Harmonic Analysis on Free Groups, Lecture Notes in Pure and Appl. Math. 87, Marcel Dekker, New York, 1983.
  8. [Hö] L. Hörmander, Estimates for translation invariant operators in Lp spaces, Acta Math. 104 (1960), 93-140.
  9. [Lo] N. Lohoué, Estimations Lp des coefficients de représentation et opérateurs de convolution, Adv. Math. 38 (1980), 178-221.
  10. [N] C. Nebbia, Groups of isometries of a tree and the Kunze-Stein phenomenon, Pacific J. Math. 133 (1988), 141-149.
  11. [Py] T. Pytlik, Radial convolutors on free groups, Studia Math. 78 (1984), 178-183.
  12. [RT] R. Rochberg and M. Taibleson, Factorization of the Green's operator and weak-type estimates for a random walk on a tree, Publ. Mat. 35 (1991), 187-207.
Colloquium Mathematicum
1999/80/1
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Pages:
53-61
Main language of publication
English
Received
1998-07-20
Published
1999
Exact and natural sciences