Representations of Jordan algebras and special functions

Giancarlo Travaglini

Colloquium Mathematicae (1991)

  • Volume: 62, Issue: 2, page 257-266
  • ISSN: 0010-1354

Abstract

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This paper is concerned with the action of a special formally real Jordan algebra U on an Euclidean space E, with the decomposition of E under this action and with an application of this decomposition to the study of Bessel functions on the self-adjoint homogeneous cone associated to U.

How to cite

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Travaglini, Giancarlo. "Representations of Jordan algebras and special functions." Colloquium Mathematicae 62.2 (1991): 257-266. <http://eudml.org/doc/210112>.

@article{Travaglini1991,
abstract = {This paper is concerned with the action of a special formally real Jordan algebra U on an Euclidean space E, with the decomposition of E under this action and with an application of this decomposition to the study of Bessel functions on the self-adjoint homogeneous cone associated to U.},
author = {Travaglini, Giancarlo},
journal = {Colloquium Mathematicae},
keywords = {representations; Jordan algebras; Bessel functions; special formally real Jordan algebra; asymptotic formula; stationary phase method},
language = {eng},
number = {2},
pages = {257-266},
title = {Representations of Jordan algebras and special functions},
url = {http://eudml.org/doc/210112},
volume = {62},
year = {1991},
}

TY - JOUR
AU - Travaglini, Giancarlo
TI - Representations of Jordan algebras and special functions
JO - Colloquium Mathematicae
PY - 1991
VL - 62
IS - 2
SP - 257
EP - 266
AB - This paper is concerned with the action of a special formally real Jordan algebra U on an Euclidean space E, with the decomposition of E under this action and with an application of this decomposition to the study of Bessel functions on the self-adjoint homogeneous cone associated to U.
LA - eng
KW - representations; Jordan algebras; Bessel functions; special formally real Jordan algebra; asymptotic formula; stationary phase method
UR - http://eudml.org/doc/210112
ER -

References

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  1. [1] H. Braun and M. Koecher, Jordan-Algebren, Springer, Berlin, 1966. 
  2. [2] J. Dorfmeister, Theta functions for the special formally real Jordan algebras, Invent. Math. 44 (1978), 103-108. Zbl0378.32019
  3. [3] J. Faraut and G. Travaglini, Bessel functions associated with representations of formally real Jordan algebras, J. Funct. Anal. 71 (1987), 123-141. Zbl0612.43009
  4. [4] M. V. Fedoryuk, The stationary phase and pseudodifferential operators, Uspekhi Mat. Nauk 26 (1) (1971), 67-112; English transl.: Russian Math. Surveys 26 (1) (1971), 65-115. Zbl0221.47036
  5. [5] K. McCrimmon, Jordan algebras and their applications, Bull. Amer. Math. Soc. 84 (1978), 612-627. Zbl0421.17010
  6. [6] I. Satake, Algebraic structure of symmetric domains, Iwanami Shoten and Princeton Univ. Press, Princeton, N.J., 1980. Zbl0483.32017

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