The Functional Equation of Zeta Distributions Associated With Non-Euclidean Jordan Algebras
Canadian journal of mathematics, Tome 58 (2006) no. 1, pp. 3-22

Voir la notice de l'article provenant de la source Cambridge University Press

This paper is devoted to the study of certain zeta distributions associated with simple non-Euclidean Jordan algebras. An explicit form of the corresponding functional equation and Bernstein-type identities is obtained.
DOI : 10.4153/CJM-2006-001-7
Mots-clés : 11M41, 17C20, 11S90, Zeta distributions, functional equations, Bernstein polynomials, non-Euclidean Jordan algebras
Saïd, Salem Ben. The Functional Equation of Zeta Distributions Associated With Non-Euclidean Jordan Algebras. Canadian journal of mathematics, Tome 58 (2006) no. 1, pp. 3-22. doi: 10.4153/CJM-2006-001-7
@article{10_4153_CJM_2006_001_7,
     author = {Sa{\"\i}d, Salem Ben},
     title = {The {Functional} {Equation} of {Zeta} {Distributions} {Associated} {With} {Non-Euclidean} {Jordan} {Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {3--22},
     year = {2006},
     volume = {58},
     number = {1},
     doi = {10.4153/CJM-2006-001-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2006-001-7/}
}
TY  - JOUR
AU  - Saïd, Salem Ben
TI  - The Functional Equation of Zeta Distributions Associated With Non-Euclidean Jordan Algebras
JO  - Canadian journal of mathematics
PY  - 2006
SP  - 3
EP  - 22
VL  - 58
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2006-001-7/
DO  - 10.4153/CJM-2006-001-7
ID  - 10_4153_CJM_2006_001_7
ER  - 
%0 Journal Article
%A Saïd, Salem Ben
%T The Functional Equation of Zeta Distributions Associated With Non-Euclidean Jordan Algebras
%J Canadian journal of mathematics
%D 2006
%P 3-22
%V 58
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2006-001-7/
%R 10.4153/CJM-2006-001-7
%F 10_4153_CJM_2006_001_7

[1] [1] Atiyah, M. F., Resolution of singularities and division of distributions. Comm. Pure Appl. Math. 23(1970), 145–150. Google Scholar

[2] [2] Angeli, Y., Analyse harmonique sur les cones satellites. Thèse, Université de Nancy, 2001. Google Scholar

[3] [3] Barchini, L., Sepanski, M., and Zierau, R., Positivity of zeta distributions and small unitary representations. Preprint (2002). Google Scholar

[4] [4] Bernstein, I. N., Analytic continuation of generalized functions with respect to a parameter. Functional Anal. Appl. 6(1972), 273–285. Google Scholar

[5] [5] Bernstein, I. N. and Gel’fand, S. I., Meromorphic property of the function Pλ. Functional Anal. Appl. 3(1969), 68–69. Google Scholar

[6] [6] Bopp, N. and Rubenthaler, H., Fonction zêta associée à la série principal sphérique de certains espaces symétriques. Ann. Sci. Ec. Norm. Sup. (4) 26(1993), 701–745. Google Scholar

[7] [7] Bopp, N. and Rubenthaler, H., Une fonction zêta associée à certaines familles d’espaces symétrique réels. C. R. Acad. Sci. Paris Sér. I Math. 325(1997), 355–360. Google Scholar

[8] [8] Clerc, J.-L., Zeta distributions associated to a representation of a Jordan algebra. Math. Z. 239(2002), 263–276. Google Scholar

[9] [9] Dvorsky, A. and Sahi, S., Explicit Hilbert spaces for certain unipotent representations. III. J. Funct. Anal. 201(2003), 430–456. Google Scholar

[10] [10] Faraut, J. and Korányi, A., Analysis on Symmetric Cones. Oxford Mathematical Monographs, Oxford University Press, Oxford, 1994. Google Scholar

[11] [11] Godment, R. and Jacquet, H., Zeta functions of simple algebras. Lecture Notes in Mathematics 260, Springer-Verlag, Berlin, 1972. Google Scholar

[12] [12] Gindikin, S. G., Invariant generalized functions in homogeneous domains. Functional. Anal. Appl. 9(1975), 50–52. Google Scholar

[13] [13] Muller, I., Décomposition orbitale des espaces préhomogènes réguliers de type parabolique commutatif et application. C. R. Acad. Sci. Paris Sér I Math. 303(1986), 495–498. Google Scholar

[14] [14] Pevsner, M., Analyse conforme sur les algebres de Jordan. Thèse, Université Paris VI 1998. Google Scholar

[15] [15] Satake, I., Algebraic Structures of Symmetric Domains. Iwanami-Shoten, Tokyo; Princeton University Press, Princeton, NJ, 1980. Google Scholar

[16] [16] Satake, I. and Faraut, J., The functional equation of zeta distributions associated with formally real Jordan algebras. Tohoku Math. J. 88(1984), 469–482. Google Scholar

[17] [17] Sato, M. and Shintani, T., On zeta functions associated with prehomogeneous vector spaces. Ann. of Math. 100(1974), 131–170. Google Scholar

[18] [18] Sato, M. and Kimura, T., A classification of irreducible prehomogeneous vector spaces and their relative invariants. Nogoya Math. J. 65(1977), 1–155. Google Scholar

[19] [19] Shintani, T., On the Dirichlet series whose coefficients are class numbers of integral cubic forms. J. Math. Soc. Japan 24(1972), 132–188. Google Scholar

[20] [20] Tate, J., Fourier analysis in number fields and Hecke's zeta function. In: Algebraic Number Theory, Thompson, Washington, D.C., 1967, pp. 305–347. Google Scholar

Cité par Sources :