Asymptotic behaviour of generalized Poisson integrals in rank one symmetric spaces and in trees

Peter Sjögren

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1988)

  • Volume: 15, Issue: 1, page 99-113
  • ISSN: 0391-173X

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Sjögren, Peter. "Asymptotic behaviour of generalized Poisson integrals in rank one symmetric spaces and in trees." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 15.1 (1988): 99-113. <http://eudml.org/doc/84027>.

@article{Sjögren1988,
author = {Sjögren, Peter},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {rank-one symmetric space; Cartan subalgebra; Lie algebra; - Poisson transform; Iwasawa decomposition; normalized Poisson transform; spherical function; Harish Chandra c-function; admissible convergence; K- finite functions; homogeneous trees},
language = {eng},
number = {1},
pages = {99-113},
publisher = {Scuola normale superiore},
title = {Asymptotic behaviour of generalized Poisson integrals in rank one symmetric spaces and in trees},
url = {http://eudml.org/doc/84027},
volume = {15},
year = {1988},
}

TY - JOUR
AU - Sjögren, Peter
TI - Asymptotic behaviour of generalized Poisson integrals in rank one symmetric spaces and in trees
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1988
PB - Scuola normale superiore
VL - 15
IS - 1
SP - 99
EP - 113
LA - eng
KW - rank-one symmetric space; Cartan subalgebra; Lie algebra; - Poisson transform; Iwasawa decomposition; normalized Poisson transform; spherical function; Harish Chandra c-function; admissible convergence; K- finite functions; homogeneous trees
UR - http://eudml.org/doc/84027
ER -

References

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  1. [1] E.P. Van Den Ban - H. Schlichtkrull, Asymptotic expansions and boundary values of eigenfunctions on Riemannian symmetric spaces. J. reine angew. Math.380 (1987), pp. 108-165. Zbl0631.58028MR916202
  2. [2] A. Figà-Talamanca - M.A. Picardello, Harmonic analysis on free groups. Marcel Dekker, 1983. Zbl0536.43001MR710827
  3. [3] G.B. Folland - E.M. Stein, Hardy spaces on homogeneous groups. Princeton University Press, 1982. Zbl0508.42025MR657581
  4. [4] S. Helgason, A duality for symmetric spaces with applications to group representations II. Differential equations and eigenspace representations. Adv. in Math.22 (1976), pp. 187-219. Zbl0351.53037MR430162
  5. [5] S. Helgason, Differential geometry, Lie groups, and symmetric spaces. Academic Press, 1978. Zbl0451.53038MR514561
  6. [6] S. Helgason, Groups and geometric analysis: Integral geometry, invariant differential operators, and spherical functions. Academic Press, 1984. Zbl0543.58001MR754767
  7. [7] A.W. Knapp - E.M. Stein, Intertwining operators for semisimple groups, II. Invent. Math.60 (1980), pp. 9-84. Zbl0454.22010MR582703
  8. [8] A. Korányi - M.A. Picardello, Boundary behaviour of eigenfunctions of the Laplace operator on trees. Ann. Scuola Norm. Sup. Pisa, 13 (1986), pp. 389-399. Zbl0621.31005MR881098
  9. [9] P. Sjögren, Convergence for the square root of the Poisson kernel. Pacific J. Math.131 (1988), pp. 361-391. Zbl0601.31001MR922224

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