B. Amri, On the integral representations for Dunkl kernels of type A 2, J. Lie Theory, vol.26, issue.4, pp.1163-1175, 2016.

B. Amri, J. Ph, &. M. Anker, and . Sifi, Three results in Dunkl analysis, Colloquium Mathematicum, vol.118, issue.1, pp.299-312, 2010.
DOI : 10.4064/cm118-1-16

URL : http://arxiv.org/pdf/0904.3608v1.pdf

B. Amri and &. , Demni : Laplace?type integral representations of the generalized Bessel function and of the Dunkl kernel of type, p.preprint, 2016.

B. Amri and &. M. Sifi, Transform??es de Riesz associ??s ?? la transform??e de Dunkl, Annales math??matiques Blaise Pascal, vol.19, issue.1, pp.247-262, 2012.
DOI : 10.5802/ambp.312

B. Amri and &. M. Sifi, Singular integral operators in Dunkl setting, J. Lie Theory, vol.22, issue.3, pp.723-739, 2012.

J. Ph, Anker : An elementary proof of the positivity of the intertwining operator in one?dimensional trigonometric Dunkl theory, preprint

J. Ph, F. Anker, and &. Ayadi, Sifi : Opdam's hypergeometric functions pproduct formula and convolution structure in dimension 1q, Adv. Pure Appl. Math, vol.3, issue.1, pp.11-44, 2012.

J. Ph, N. B. Anker, J. Salem, &. N. Dziuba?ski, and . Hamda, The Hardy space H 1 in the rational Dunkl setting, Constr. Approx, vol.42, issue.1, pp.93-128, 2015.

J. Ph, E. Anker, &. Damek, and . Ch, Yacoub : Spherical analysis on harmonic AN groups, Ann. Scuola Norm. Sup. Pisa, vol.23, issue.4 4, pp.643-679, 1996.

J. Ph, P. Anker, E. Martinot, &. A. Pedon, and . Setti, The shifted wave equation on Damek?Ricci spaces and on homogeneous trees, in Trends in Harmonic Analysis, XXXV Convegno di Analisi Armonica, pp.1-25, 2011.

J. Ph, &. P. Anker, and . Ostellari, The heat kernel on symmetric spaces, in Lie groups and symmetric spaces (in memory of F.I. Karpelevich), Amer. Math. Soc. Transl, issue.2, pp.27-46, 2004.

J. Ph, B. Anker, and &. Schapira, Trojan : Heat kernel and Green function estimates on affine buildings of type r A r , preprint

S. , B. Saïd, and &. , Ørsted : Bessel functions for root systems via the trigonometric setting, Int. Math. Res. Not. (IMRN), vol.9, pp.551-585, 2005.

S. B. Saïd, T. Kobayashi, and &. , Abstract, Compositio Mathematica, vol.85, issue.04, pp.1265-1336, 2012.
DOI : 10.1142/S0219530503000132

I. Cherednik, Double affine Hecke algebras, Soc. Lect. Note Ser, vol.319, p.434, 2005.
DOI : 10.1017/CBO9780511546501

D. Constales, H. De-bie, and &. P. Lian, Explicit formulas for the Dunkl dihedral kernel and the p?,aq? generalized Fourier kernel , preprint

M. G. Cowling, S. Meda, and &. A. Setti, An overview of harmonic analysis on the group of isometries of a homogeneous tree, Expo. Math, vol.16, pp.385-423, 1998.

M. G. Cowling, S. Meda, and &. A. Setti, Estimates for functions of the Laplace operator on homogeneous trees, Transactions of the American Mathematical Society, vol.352, issue.09, pp.4271-4293, 2000.
DOI : 10.1090/S0002-9947-00-02460-0

L. Deléaval, N. Demni, and &. H. Youssfi, Dunkl kernel associated with dihedral groups, Journal of Mathematical Analysis and Applications, vol.432, issue.2, pp.928-944, 2015.
DOI : 10.1016/j.jmaa.2015.07.029

N. Demni, Dunkl operators (an overview ) Updated lecture notes (2015), CIMPA Spring School Analytical and probabilistic aspects of Dunkl theory (Monastir, 2009.

C. F. Dunkl and &. Y. Xu, Orthogonal polynomials of several variables, Encyclopedia Math, Appl, vol.81, 2001.

J. Dziuba?ski, Riesz Transforms Characterizations of Hardy Spaces $$H^1$$ H 1 for the Rational Dunkl Setting and Multidimensional Bessel Operators, The Journal of Geometric Analysis, vol.262, issue.2, pp.2639-2663, 2016.
DOI : 10.1007/s12220-015-9642-2

P. Etingof, Calogero?Moser systems and representation theory, Zurich Lect, Adv. Math. Eur. Math. Soc, vol.4, 2007.
DOI : 10.4171/034

P. Etingof, A uniform proof of the Macdonald-Mehta-Opdam identity for finite Coxeter groups, Mathematical Research Letters, vol.17, issue.2, pp.275-282, 2010.
DOI : 10.4310/MRL.2010.v17.n2.a7

J. Faraut, Analyse harmonique sur les paires de Guelfand et les espaces hyperboliques, pp.315-446, 1982.

A. Figà, ?. Talamanca, and &. M. Picardello, Harmonic analysis on free groups, Lect. Notes Pure Appl. Math, vol.87, 1983.

L. Gallardo and &. L. Godefroy, Propri??t?? de Liouville et ??quation de Poisson pour le laplacien g??n??ralis?? de Dunkl, Comptes Rendus Mathematique, vol.337, issue.10, pp.639-644, 2003.
DOI : 10.1016/j.crma.2003.09.032

L. Gallardo and &. , A new mean value property for harmonic functions relative to the Dunkl-Laplacian operator and applications, Transactions of the American Mathematical Society, vol.368, issue.5, pp.3727-3753, 2016.
DOI : 10.1090/tran/6671

L. Gallardo and &. , Rejeb : Newtonian potentials and subharmonic functions associated to the Dunkl? Laplace operator, p.1368871
DOI : 10.1007/s11118-017-9619-9

URL : https://hal.archives-ouvertes.fr/hal-01368871/document

L. Gallardo and &. C. Rejeb, Support properties of the intertwining and the mean value operators in Dunkl's analysis, p.1331693

L. Gallardo and &. K. Trimèche, Positivity of the Jacobi???Cherednik intertwining operator and its dual, Advances in Pure and Applied Mathematics, vol.1, issue.2, pp.163-194, 2010.
DOI : 10.1515/apam.2010.011

R. Gangolli and &. V. Varadarajan, Harmonic analysis of spherical functions on real reductive groups, 1988.
DOI : 10.1007/978-3-642-72956-0

P. Graczyk, T. Luks, and &. , Rösler : On the Green function and Poisson integrals of the Dunkl Laplacian, preprint

M. Hallnäs and &. S. , Ruijsenaars : A recursive construction of joint eigenfunctions for the hyperbolic nonrelativistic Calogero?Moser Hamiltonians, Int. Math. Res. Not. (IMRN), vol.20, pp.10278-10313, 2015.

G. J. Heckman, An elementary approach to the hypergeometric shift operators of Opdam, Inventiones Mathematicae, vol.15, issue.4, pp.341-350, 1991.
DOI : 10.1007/BF01239517

G. J. Heckman and &. H. Schlichtkrull, Harmonic analysis and special functions on symmetric spaces, Perspect. Math, vol.16, 1994.

S. Helgason, Groups and geometric analysis (Integral geometry, invariant differential operators, and spherical functions), Pure Appl, Math. Math. Surveys Monographs, vol.113, issue.83, 1984.

J. E. Humphreys, Reflection groups and Coxeter groups, Cambridge Studies Adv. Math, vol.29, 1990.
DOI : 10.1017/CBO9780511623646

A. and J. Eddine, Schrödinger equation on homogeneous trees, J. Lie Theory, vol.23, pp.779-794, 2013.

M. F. De-jeu, Paley?Wiener theorems for the Dunkl transform, Transactions of the American Mathematical Society, vol.358, issue.10, pp.4225-4250, 2006.
DOI : 10.1090/S0002-9947-06-03960-2

M. De-jeu and &. M. Rösler, Asymptotic analysis for the Dunkl kernel, J. Approx. Theory, vol.119, pp.110-126, 2002.

R. Kane, Reflection groups and invariant theory, CMS Books Math, vol.5, 2001.
DOI : 10.1007/978-1-4757-3542-0

T. H. Koornwinder, Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups, Special functions, pp.1-84, 1984.
DOI : 10.1007/978-94-010-9787-1_1

B. Krötz and &. E. Opdam, Analysis on the Crown Domain, Geometric and Functional Analysis, vol.18, issue.4, pp.1326-1421, 2008.
DOI : 10.1007/s00039-008-0684-5

I. G. Macdonald, Spherical functions on a group of p?adic type, Publ. Ramanujan Institute 2, Centre Adv. Study Math, 1971.

I. G. Macdonald, Affine Hecke algebras and orthogonal polynomials, Cambridge Tracts Math, 2003.
DOI : 10.1017/cbo9780511542824

URL : http://archive.numdam.org/article/SB_1994-1995__37__189_0.pdf

A. M. Mantero and &. , Macdonald formula for spherical functions on affine buildings, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.20, issue.4, pp.669-758, 2011.
DOI : 10.5802/afst.1321

M. Maslouhi and &. E. Youssfi, Harmonic functions associated to Dunkl operators, Monatshefte f??r Mathematik, vol.12, issue.4, pp.337-345, 2007.
DOI : 10.1007/s00605-007-0475-3

G. Medolla and &. A. Setti, The wave equation on homogeneous trees, Annali di Matematica Pura ed Applicata, vol.64, issue.6, pp.1-27, 1999.
DOI : 10.1007/BF02505986

H. Mejjaoli and &. , On a mean value property associated with the dunkl laplacian operator and applications, Integral Transforms and Special Functions, vol.60, issue.3, pp.279-302, 2001.
DOI : 10.4153/CJM-1998-010-9

E. K. Narayanan, A. Pasquale, and &. S. Pusti, Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications, Advances in Mathematics, vol.252, pp.227-259, 2014.
DOI : 10.1016/j.aim.2013.10.027

URL : https://hal.archives-ouvertes.fr/hal-01096768

A. Okounkov and &. G. Olshanski, Shifted jack polynomials, binomial formula, and applications, Mathematical Research Letters, vol.4, issue.1, pp.69-78, 1997.
DOI : 10.4310/MRL.1997.v4.n1.a7

URL : http://arxiv.org/abs/q-alg/9608020

E. M. Opdam, Some applications of hypergeometric shift operators, Inventiones Mathematicae, vol.3, issue.1, pp.1-18, 1989.
DOI : 10.1007/BF01388841

E. M. Opdam, Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group, Compos. Math, vol.85, pp.333-373, 1993.

E. M. Opdam, Harmonic analysis for certain representations of graded Hecke algebras, Acta Mathematica, vol.175, issue.1, pp.75-121, 1995.
DOI : 10.1007/BF02392487

E. M. Opdam, Lecture notes on Dunkl operators for real and complex reflection groups, Math. Soc. Japan Mem. Math. Soc. Japan, vol.8, 2000.
DOI : 10.2969/msjmemoirs/008010000

J. Parkinson, Spherical harmonic analysis on affine buildings, Mathematische Zeitschrift, vol.56, issue.3, pp.571-606, 2006.
DOI : 10.1017/S1446788700035540

URL : http://arxiv.org/abs/math/0604058

C. Rejeb, Fonctions harmoniques et sous?harmoniques associées à des systèmes de racines, 2015.

M. Rösler, Dunkl Operators: Theory and Applications, Orthogonal polynomials and special functions, pp.93-135, 2002.
DOI : 10.1007/3-540-44945-0_3

M. Rösler, A positive radial product formula for the Dunkl kernel, Transactions of the American Mathematical Society, vol.355, issue.06, pp.2413-2438, 2003.
DOI : 10.1090/S0002-9947-03-03235-5

M. Rösler, Bessel convolutions on matrix cones, Compositio Mathematica, vol.143, issue.03, pp.749-779, 2007.
DOI : 10.1112/S0010437X06002594

M. Rösler, Positive convolution structure for a class of Heckman???Opdam hypergeometric functions of type BC, Journal of Functional Analysis, vol.258, issue.8, pp.2779-2800, 2010.
DOI : 10.1016/j.jfa.2009.12.007

M. Rösler, T. H. Koornwinder, and &. , Abstract, Compositio Mathematica, vol.4, issue.08, pp.1381-1400, 2013.
DOI : 10.1016/0001-8708(89)90015-7

M. Rösler and &. M. Voit, Positivity of Dunkl's intertwining operator via the trigonometric setting, Int. Math. Res. Not. (IMRN), vol.63, pp.3379-3389, 2004.

M. Rösler and &. , Voit : A limit relation for Dunkl?Bessel functions of type A and B, Symmetry Integrability Geom, Meth. Appl. (SIGMA), vol.4, p.83, 2008.

M. Rösler and &. M. Voit, Integral representation and uniform limits for some Heckman-Opdam hypergeometric functions of type \textsl{BC}, Transactions of the American Mathematical Society, vol.368, issue.8, pp.6005-6032, 2016.
DOI : 10.1090/tran6673

F. Rouvière, Espaces de Damek-Ricci, géométrie et analyse, Analyse sur les groupes de Lie et théorie des représentations, pp.45-100, 1999.

P. Sawyer, Spherical functions on symmetric cones, Transactions of the American Mathematical Society, vol.349, issue.09, pp.3569-3584, 1997.
DOI : 10.1090/S0002-9947-97-01505-5

P. Sawyer, A Laplace?type representation of the generalized spherical functions associated to the root systems of type A, preprint

B. Schapira, Etude analytique et probabiliste de laplaciens associés à des systèmes de racines plaplacien hypergéométrique de Heckman?Opdam et laplacien combinatoire sur les immeubles affinesq, 2006.

B. Schapira, The Heckman???Opdam Markov processes, Probability Theory and Related Fields, vol.21, issue.4, pp.495-519, 2007.
DOI : 10.1007/s00440-006-0034-1

URL : https://hal.archives-ouvertes.fr/hal-00150394

B. Schapira, Contributions to the Hypergeometric Function Theory of Heckman and Opdam: Sharp Estimates, Schwartz Space, Heat Kernel, Geometric and Functional Analysis, vol.18, issue.1, pp.222-250, 2008.
DOI : 10.1007/s00039-008-0658-7

URL : https://hal.archives-ouvertes.fr/hal-00023581

B. Schapira, Bounded Harmonic Functions for the Heckman-Opdam Laplacian, International Mathematics Research Notices, vol.17, pp.3149-3159, 2009.
DOI : 10.1093/imrn/rnp046

URL : https://hal.archives-ouvertes.fr/hal-00324368

Y. Sun, A new integral formula for Heckman???Opdam hypergeometric functions, Advances in Mathematics, vol.289, pp.1157-1204, 2016.
DOI : 10.1016/j.aim.2015.09.037

URL : http://arxiv.org/abs/1406.3772

S. Thangavelu and &. Y. Xu, Convolution operator and maximal function for the Dunkl transform, Journal d'Analyse Math??matique, vol.29, issue.1, pp.25-55, 2005.
DOI : 10.1007/BF02807401

K. Trimèche, The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman???Opdam theory, Advances in Pure and Applied Mathematics, vol.1, issue.3, pp.293-323, 2010.
DOI : 10.1515/apam.2010.015

K. Trimèche, Hypergeometric convolution structure on L p ?spaces and applications for the Heckman- Opdam theory, p.preprint, 2012.

K. Trimèche, Positivity of the transmutation operators and absolute continuity of their representing measures for a root system on R d, Int. J. Appl. Math, vol.28, issue.4, pp.427-453, 2015.

B. Trojan, Heat kernel and Green function estimates on affine buildings, preprint

M. Voit, Product formulas for a two?parameter family of Heckman?Opdam hypergeometric functions of type BC, J. Lie Theory, vol.25, issue.1, pp.9-36, 2015.