Zonal spherical function

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For zonal spherical functions see Spherical harmonics.^[1]
Zonal spherical functions have been explicitly determined for real semisimple groups by Harish-Chandra.^[2]
The abstract functional analytic theory of zonal spherical functions was first developed by Roger Godement.^[2]
For semisimple p-adic Lie groups, the theory of zonal spherical functions and Hecke algebras was first developed by Satake and Ian G. Macdonald.^[2]
Properties 2, 3 and 4 or properties 3, 4 and 5 characterize zonal spherical functions.^[2]

Previous work characterized certain left coideal subalgebras in the quantized enveloping algebra and established an appropriate framework for quantum zonal spherical functions.^[1]
The zonal spherical functions are a broad extension of the notion of zonal spherical harmonics to allow for a more general symmetry group.^[2]
Zonal spherical functions have been explicitly determined for real semisimple groups by Harish-Chandra.^[3]
The abstract functional analytic theory of zonal spherical functions was first developed by Roger Godement.^[3]
For semisimple p-adic Lie groups, the theory of zonal spherical functions and Hecke algebras was first developed by Satake and Ian G. Macdonald.^[3]
Properties 2, 3 and 4 or properties 3, 4 and 5 characterize zonal spherical functions.^[3]
I tried to rotate zonal spherical function, projected onto spherical harmonic basis.^[4]
For zonal spherical functions see Spherical harmonics.^[5]
But to determine the explicitform of zonal spherical functions and the Plancherel measure, it seems necessary toknow the (infinite) matrix of this Fourier transformation more explicitly.^[6]
3 zonal spherical functions k(x), k(y) = Gk(x, y), where Gk are Gegenbauer polynomials, zonal spherical functions associated with Harmk(Sd1).^[7]
4 zonal spherical functions k(x), k(y) = Gk(x, y), where Gk are Gegenbauer polynomials, zonal spherical functions associated with Harmk(Sd1).^[7]