Matrix Valued Spherical Functions Associated to the Complex Projective Plane
نویسندگان
چکیده
منابع مشابه
Matrix Valued Spherical Functions Associated to the Complex Projective Plane
The main purpose of this paper is to compute all irreducible spherical functions on G = SU(3) of arbitrary type δ ∈ K̂, where K = S(U(2) × U(1)) ≃ U(2). This is accomplished by associating to a spherical function Φ on G a matrix valued function H on the complex projective plane P2(C) = G/K. It is well known that there is a fruitful connection between the hypergeometric function of Euler and Gaus...
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The classical (scalar valued) theory of spherical functions (put forward by Cartan and others after him) allows one to unify under one roof a number of examples that were very well known before the theory was formulated. These examples include many special functions like Jacobi polynomials, Bessel functions, Laguerre polynomials, Hermite polynomials, Legendre functions, etc. All these functions...
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The main purpose of this paper is to compute all irreducible spherical functions on G = SL(2,C) of arbitrary type δ ∈ K̂, where K = SU(2). This is accomplished by associating to a spherical function Φ on G a matrix valued function H on the three dimensional hyperbolic space H = G/K. The entries of H are solutions of two coupled systems of ordinary differential equations. By an appropriate twisti...
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The main purpose of this paper is to obtain an explicit expression of a family of matrix valued orthogonal polynomials {Pn}n, with respect to a weight W , that are eigenfunctions of a second order differential operator D. The weight W and the differential operator D were found in [12], using some aspects of the theory of the spherical functions associated to the complex projective spaces. We al...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2002
ISSN: 0022-1236
DOI: 10.1006/jfan.2001.3840