Eigenfunctions of the Laplace operators for buildings of type B ~ 2

A. M. Mantero; A. Zappa

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 1, page 163-195
  • ISSN: 0392-4041

Abstract

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We consider for an affine building of type B ~ 2 Helgason's conjecture with respect to Laplace operators defined over different types of vertices. We prove that there are cases in which the conjecture fails, since there exist eigenfunctions which are not the Poisson transform of finitely additive measures at the maximal boundary of the building.

How to cite

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Mantero, A. M., and Zappa, A.. "Eigenfunctions of the Laplace operators for buildings of type $\tilde{B}_2$." Bollettino dell'Unione Matematica Italiana 5-B.1 (2002): 163-195. <http://eudml.org/doc/196100>.

@article{Mantero2002,
abstract = {We consider for an affine building of type $\tilde\{B\}_2$ Helgason's conjecture with respect to Laplace operators defined over different types of vertices. We prove that there are cases in which the conjecture fails, since there exist eigenfunctions which are not the Poisson transform of finitely additive measures at the maximal boundary of the building.},
author = {Mantero, A. M., Zappa, A.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {163-195},
publisher = {Unione Matematica Italiana},
title = {Eigenfunctions of the Laplace operators for buildings of type $\tilde\{B\}_2$},
url = {http://eudml.org/doc/196100},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Mantero, A. M.
AU - Zappa, A.
TI - Eigenfunctions of the Laplace operators for buildings of type $\tilde{B}_2$
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/2//
PB - Unione Matematica Italiana
VL - 5-B
IS - 1
SP - 163
EP - 195
AB - We consider for an affine building of type $\tilde{B}_2$ Helgason's conjecture with respect to Laplace operators defined over different types of vertices. We prove that there are cases in which the conjecture fails, since there exist eigenfunctions which are not the Poisson transform of finitely additive measures at the maximal boundary of the building.
LA - eng
UR - http://eudml.org/doc/196100
ER -

References

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  1. CARTWRIGHT, D. I., A Brief Introduction to Buildings, Contemporary Mathematics, Vol. 206 (1997), 45-77. Zbl0943.51011MR1463728
  2. FEIT, W.- HIGMAN, G., The nonexistence of certain generalized polygons, J. Algebra, 1 (1964), 114-131. Zbl0126.05303MR170955
  3. HIGMAN, D. G., Invariant relations, coherent configurations and generalized polygons, Combinatorics part 3 (ed. M. Hall and J. Van Lint), Reidel, Dordrecht1975, 247-263. Zbl0366.05018MR379244
  4. KATO, S., On eigenspaces of the Hecke algebra with respect to a good maximal compact subgroup of a p -adic reductive group, Math. Ann., 257 (1981), 1-7. Zbl0452.43014MR630642
  5. MANTERO, A. M.- ZAPPA, A., Eigenfunctions of the Laplace Operators for a Building of type A ~ 2 , J. of Geom. Anal., 10 (2000), 339-363. Zbl0986.22009MR1766487
  6. MANTERO, A. M.- ZAPPA, A., Eigenfunctions of the Laplace Operators for a Building of type G ~ 2 , preprint. MR2537284
  7. RONAN, M. A., Lectures on Buildings, Perspectives in Math.7, Academic Press, London1989. Zbl0694.51001MR1005533

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