منابع مشابه
Spherical Functions on Symmetric Cones
In this note, we obtain a recursive formula for the spherical functions associated with the symmetric cone of a formally real Jordan algebra. We use this formula as an inspiration for a similar recursive formula involving the Jack polynomials.
متن کاملThe Asymptotic Expansion of Spherical Functions on Symmetric Cones
In [7], Genkai Zhang gives the asymptotic expansion for the spherical functions on symmetric cones. This is done to prove a central limit theorem for these spaces. The work of Zhang is a natural continuation of the work of Audrey Terras [6] (the case of the positive definite matrices of rank 2) and of the work of Donald St.P. Richards [3] (the case of the positive definite matrices of all ranks...
متن کاملSpherical Functions and Spherical Laplace Transform on Ordered Symmetric Space
Let G=H be a semisimple globally hyperbolic symmetric space and let ' be a H-spherical function on G=H. We derive an expansion formula for ' similar to the Harish-Chandra formula for spherical functions on a Riemannian symmetric space. We use this result to analytically continuate the spherical functions in the parameters. A functional equation for ' is derived and then used to invert the spher...
متن کاملLattice Point Generating Functions and Symmetric Cones
Abstract. We show that a recent identity of Beck–Gessel–Lee–Savage on the generating function of symmetrically contrained compositions of integers generalizes naturally to a family of convex polyhedral cones that are invariant under the action of a finite reflection group. We obtain general expressions for the multivariate generating functions of such cones, and work out their general form more...
متن کاملDifferential Recursion Relations for Laguerre Functions on Symmetric Cones
Let Ω be a symmetric cone and V the corresponding simple Euclidean Jordan algebra. In [2, 5, 6, 8] we considered the family of generalized Laguerre functions on Ω that generalize the classical Laguerre functions on R. This family forms an orthogonal basis for the subspace of L-invariant functions in L(Ω, dμν), where dμν is a certain measure on the cone and where L is the group of linear transfo...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1997
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-97-01505-5