Eigenfunctions of the Laplace Operators for a Building of Type G ~ 2

A. M. Mantero; A. Zappa

Bollettino dell'Unione Matematica Italiana (2009)

  • Volume: 2, Issue: 2, page 483-508
  • ISSN: 0392-4041

Abstract

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Let Δ be thick affine building of type G ~ 2 the Laplace operators of Δ ; associated with a pair ( y 1 , y 2 ) ; is the Poisson transform of a suitable finitely additive measure on the maximal boundary Ω of Δ ; by using only the combinatorial structure of Δ .

How to cite

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Mantero, A. M., and Zappa, A.. "Eigenfunctions of the Laplace Operators for a Building of Type $\widetilde{G}_{2}$." Bollettino dell'Unione Matematica Italiana 2.2 (2009): 483-508. <http://eudml.org/doc/290580>.

@article{Mantero2009,
abstract = {Let $\Delta$ be thick affine building of type $\widetilde\{G\}_\{2\}$ the Laplace operators of $\Delta$; associated with a pair $(y_\{1\}, y_\{2\})$; is the Poisson transform of a suitable finitely additive measure on the maximal boundary $\Omega$ of $\Delta$; by using only the combinatorial structure of $\Delta$.},
author = {Mantero, A. M., Zappa, A.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {483-508},
publisher = {Unione Matematica Italiana},
title = {Eigenfunctions of the Laplace Operators for a Building of Type $\widetilde\{G\}_\{2\}$},
url = {http://eudml.org/doc/290580},
volume = {2},
year = {2009},
}

TY - JOUR
AU - Mantero, A. M.
AU - Zappa, A.
TI - Eigenfunctions of the Laplace Operators for a Building of Type $\widetilde{G}_{2}$
JO - Bollettino dell'Unione Matematica Italiana
DA - 2009/6//
PB - Unione Matematica Italiana
VL - 2
IS - 2
SP - 483
EP - 508
AB - Let $\Delta$ be thick affine building of type $\widetilde{G}_{2}$ the Laplace operators of $\Delta$; associated with a pair $(y_{1}, y_{2})$; is the Poisson transform of a suitable finitely additive measure on the maximal boundary $\Omega$ of $\Delta$; by using only the combinatorial structure of $\Delta$.
LA - eng
UR - http://eudml.org/doc/290580
ER -

References

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  9. KASHIWARA, M. - KOWATA, A. - MINEMURA, K. - OKAMOTO, K. - OSHIMA, T. - TANAKA, M., Eigenfunctions of invariant differential operators on a symmetric space, Ann. Math., 107 (1978), 1-39. Zbl0377.43012MR485861DOI10.2307/1971253
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  11. MANTERO, A. M. - ZAPPA, A., The Poisson transform on free groups and uniformly bounded representations, J. Functional Anal., 51 (1983), 372-399. Zbl0532.43006MR703084DOI10.1016/0022-1236(83)90019-8
  12. MANTERO, A. M. - ZAPPA, A., Eigenfunctions of the Laplace Operators for a Building of type A ~ 2 , J. of Geom. Anal., 10 (2) (2000), 339-363. Zbl0986.22009MR1766487DOI10.1007/BF02921829
  13. MANTERO, A. M. - ZAPPA, A., Eigenfunctions of the Laplace Operators for a Building of type B ~ 2 , Boll. U.M.I., 5-B (8) (2002), 163-195. Zbl1177.51010MR1881930
  14. MANTERO, A. M. - ZAPPA, A., Laplace operators on special vertices of type 0 in A ~ 2 buildings, preprint. Zbl1387.51013
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  16. TITS, J., Reductive groups over local fields, Proc. Symp. Pure Math., vol. 33(Automorphic forms, representations and L-functions, Corvallis 1977) (1979), 29-69. MR546588

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