Laguerre functions on symmetric cones and recursion relations in the real case
نویسندگان
چکیده
منابع مشابه
Laguerre Functions on Symmetric Cones and Recursion Relations in the Real Case
In this article we derive differential recursion relations for the Laguerre functions on the cone Ω of positive definite real matrices. The highest weight representations of the group Sp(n,R) play a fundamental role. Each such representation acts on a Hilbert space of holomorphic functions on the tube domain Ω+ iSym(n,R). We then use the Laplace transform to carry the Lie algebra action over to...
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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...
متن کاملDifferential Recursion Relations for Laguerre Functions on Hermitian Matrices
Abstract. In our previous papers [1, 2] we studied Laguerre functions and polynomials on symmetric cones Ω = H/L. The Laguerre functions l n , n ∈ Λ, form an orthogonal basis in L(Ω, dμν ) and are related via the Laplace transform to an orthogonal set in the representation space of a highest weight representations (πν ,Hν) of the automorphism group G corresponding to a tube domain T (Ω). In thi...
متن کاملSpherical 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.
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2007
ISSN: 0377-0427
DOI: 10.1016/j.cam.2005.12.002