Boundary behaviour of eigenfunctions of the Laplace operator on trees

Adam Korányi; Massimo A. Picardello

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1986)

  • Volume: 13, Issue: 3, page 389-399
  • ISSN: 0391-173X

How to cite

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Korányi, Adam, and Picardello, Massimo A.. "Boundary behaviour of eigenfunctions of the Laplace operator on trees." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 13.3 (1986): 389-399. <http://eudml.org/doc/83984>.

@article{Korányi1986,
author = {Korányi, Adam, Picardello, Massimo A.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Fatou theorem; harmonic; nontangential boundary limits; trees; Laplace operator; positive eigenfunction; Poisson kernels; Poisson integrals of finite measures},
language = {eng},
number = {3},
pages = {389-399},
publisher = {Scuola normale superiore},
title = {Boundary behaviour of eigenfunctions of the Laplace operator on trees},
url = {http://eudml.org/doc/83984},
volume = {13},
year = {1986},
}

TY - JOUR
AU - Korányi, Adam
AU - Picardello, Massimo A.
TI - Boundary behaviour of eigenfunctions of the Laplace operator on trees
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1986
PB - Scuola normale superiore
VL - 13
IS - 3
SP - 389
EP - 399
LA - eng
KW - Fatou theorem; harmonic; nontangential boundary limits; trees; Laplace operator; positive eigenfunction; Poisson kernels; Poisson integrals of finite measures
UR - http://eudml.org/doc/83984
ER -

References

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  1. [1] P. Cartier, Fonctions harmoniques sur un arbre, Sympos. Math., 9 (1972), pp. 203-270. Zbl0283.31005MR353467
  2. [2] A. Figà-Talamanca - M.A. Picardello, Harmonic analysis on free groups, Lecture Notes in Pure and Appl. Math., vol. 87, Marcel Dekker, New York, 1983. Zbl0536.43001MR710827
  3. [3] A. Korányi, Boundary behaviour of Poisson integrals on symmetric spaces, Trans. Amer. Math. Soc., 140 (1969), pp. 393-409. Zbl0179.15103MR245826
  4. [4] A. Korányi - S. Vagi, Singular integrals on homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 25 (1971), pp. 575-618. Zbl0291.43014MR463513
  5. [5] A.M. Mantero - A. Zappa, The Poisson transform and representations of free groups, J. Funct. Anal., 51 (1983), pp. 372-399. Zbl0532.43006MR703084
  6. [6] H.L. Michelson, Fatou theorem for eigenfunctions of the invariant differential operators on symmetric spaces, Trans. Amer. Math. Soc., 177 (1973), pp. 257-274. Zbl0225.31002MR319113
  7. [7] P. Sjögren, Une remarque sur la convergence des fonctions propres du Laplacien à valeur propre critique, Lecture Notes in Math. 1096, pp. 544-548, Springer, Berlin, 1984. Zbl0563.31003MR890377
  8. [8] M. Taibleson, Fourier analysis on local fields, Princeton University Press, Princeton, 1975. Zbl0319.42011MR487295
  9. [9] J.C. Taylor, An elementary proof of the theorem of Fatou-Naïm-Doob, Canad. Math. Soc. Conference Proc., vol. 1: Harmonic Analysis, Amer. Math. Soc., Providence (1981), pp. 153-163. Zbl0551.31004MR670103
  10. [10] A. Zygmund, Trigonometric series, 2nd edition, Cambridge, 1959. Zbl0367.42001

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