Invariant operators on function spaces on homogeneous trees

Michael Cowling; Stefano Meda; Alberto Setti

Colloquium Mathematicae (1999)

  • Volume: 80, Issue: 1, page 53-61
  • ISSN: 0010-1354

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Cowling, Michael, Meda, Stefano, and Setti, Alberto. "Invariant operators on function spaces on homogeneous trees." Colloquium Mathematicae 80.1 (1999): 53-61. <http://eudml.org/doc/210705>.

@article{Cowling1999,
author = {Cowling, Michael, Meda, Stefano, Setti, Alberto},
journal = {Colloquium Mathematicae},
keywords = {spherical functions; harmonic analysis; homogeneous trees; homogeneous tree; homogeneous space; convolution operators; radial functions; spherical Fourier transforms},
language = {eng},
number = {1},
pages = {53-61},
title = {Invariant operators on function spaces on homogeneous trees},
url = {http://eudml.org/doc/210705},
volume = {80},
year = {1999},
}

TY - JOUR
AU - Cowling, Michael
AU - Meda, Stefano
AU - Setti, Alberto
TI - Invariant operators on function spaces on homogeneous trees
JO - Colloquium Mathematicae
PY - 1999
VL - 80
IS - 1
SP - 53
EP - 61
LA - eng
KW - spherical functions; harmonic analysis; homogeneous trees; homogeneous tree; homogeneous space; convolution operators; radial functions; spherical Fourier transforms
UR - http://eudml.org/doc/210705
ER -

References

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  1. [BL] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Grundlehren Math. Wiss. 223, Springer, New York, 1976. Zbl0344.46071
  2. [CS] J.-L. Clerc and E. M. Stein, L p multipliers for noncompact symmetric spaces, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 3911-3912. Zbl0296.43004
  3. [CGM] M. Cowling, S. Giulini and S. Meda, L p - L q estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. I, Duke Math. J. 72 (1993), 109-150. Zbl0807.43002
  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. Zbl0949.43008
  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. Zbl0915.43007
  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. Zbl1154.22301
  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. Zbl0536.43001
  8. [Hö] L. Hörmander, Estimates for translation invariant operators in L p spaces, Acta Math. 104 (1960), 93-140. Zbl0093.11402
  9. [Lo] N. Lohoué, Estimations L p des coefficients de représentation et opérateurs de convolution, Adv. Math. 38 (1980), 178-221. Zbl0463.43003
  10. [N] C. Nebbia, Groups of isometries of a tree and the Kunze-Stein phenomenon, Pacific J. Math. 133 (1988), 141-149. Zbl0646.43006
  11. [Py] T. Pytlik, Radial convolutors on free groups, Studia Math. 78 (1984), 178-183. Zbl0572.43002
  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. Zbl0729.60008

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