Journal of Lie Theory

no. 3
Asymptotic Harmonic Analysis on the Space of Square Complex Matrices
Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 645-670
This paper is largely of expository nature. We determine the spherical functions of positive type on the space $V_\infty= M(\infty, {\bf C})$ relatively to the action of the product group $K_\infty = U(\infty)\times U(\infty)$. The space $V_\infty$ is the inductive limit of the spaces of square complex matrices $V_n=M(n, {\bf C})$, and the group $K_\infty$ is the inductive limit of the product groups $K_n=U(n) \times U(n)$, where $U(n)$ is the unitary group.
DOI: 10.5802/jolt.517
Classification: 22E30, 43A35, 43A85, 43A90
Keywords: Square complex matrices, unitary group, inductive limit, function of positive type, spherical function, ergodic measure, generalized Bochner theorem 
@article{JOLT_2008_18_3_a10,
     author = {M. Rabaoui},
     title = {Asymptotic {Harmonic} {Analysis} on the {Space} of {Square} {Complex} {Matrices}},
     journal = {Journal of Lie Theory},
     pages = {645--670},
     year = {2008},
     volume = {18},
     number = {3},
     doi = {10.5802/jolt.517},
     zbl = {1167.22008},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.517/}
}
TY  - JOUR
AU  - M. Rabaoui
TI  - Asymptotic Harmonic Analysis on the Space of Square Complex Matrices
JO  - Journal of Lie Theory
PY  - 2008
SP  - 645
EP  - 670
VL  - 18
IS  - 3
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.517/
DO  - 10.5802/jolt.517
ID  - JOLT_2008_18_3_a10
ER  - 
%0 Journal Article
%A M. Rabaoui
%T Asymptotic Harmonic Analysis on the Space of Square Complex Matrices
%J Journal of Lie Theory
%D 2008
%P 645-670
%V 18
%N 3
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.517/
%R 10.5802/jolt.517
%F JOLT_2008_18_3_a10
M. Rabaoui. Asymptotic Harmonic Analysis on the Space of Square Complex Matrices. Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 645-670. doi: 10.5802/jolt.517

Cited by Sources: