MATRIX VALUED SPHERICAL FUNCTIONS ASSOCIATED TO THE THREE DIMENSIONAL HYPERBOLIC SPACE

DOI10.1142/S0129167X02001460zbMath1048.22005arXivmath/0203211MaRDI QIDQ4807420

Inés Pacharoni, Juan Tirao, F. Alberto Gruenbaum

Publication date: 18 May 2003

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0203211

zbMATH Keywords

Hahn polynomialsspherical functions of type \(\delta\)matrix valued bispectral property

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Semisimple Lie groups and their representations (22E46) Spherical harmonics (33C55) Categorical methods for abstract harmonic analysis (43A95)

Related Items

Matrix orthogonal polynomials whose derivatives are also orthogonal ⋮ Matrix bispectrality and noncommutative algebras: beyond the prolate spheroidals ⋮ A noncommutative version of the bispectral problem. ⋮ Two stochastic models of a random walk in the \(\mathrm U(n)\)-spherical duals of \(U(n+1)\) ⋮ Spherical functions associated with the three-dimensional sphere ⋮ Spherical analysis on homogeneous vector bundles of the 3-dimensional Euclidean motion group ⋮ Matrix spherical analysis on nilmanifolds ⋮ SPHERICAL FUNCTIONS, THE COMPLEX HYPERBOLIC PLANE AND THE HYPERGEOMETRIC OPERATOR ⋮ Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory.

Cites Work

• Differential equations in the spectral parameter
• An analogue of the Paley-Wiener theorem for certain function spaces on SL(2,C)
• Matrix valued spherical functions associated to the complex projective plane
• A matrix-valued solution to Bochner's problem