Kernel Approximation on Compact Homogeneous Spaces

This thesis is concerned with approximation on compact homogeneous spaces. The first part of the research involves a particular kind of compact homogeneous space, the hypersphere, S ͩˉ¹ embedded in R ͩ. It is a calculation of three integrals associated with approximation using radial basis functions, calculating the Fourier-Gegenbauer coefficients for two such functions. The latter part of the research is a calculation of an error bound for compact homogeneous spaces when interpolating with a G-invariant kernel, a generalisation of a result already known for spheres.