%0 DATA
%A Carl Richard, Odell
%D 2012
%T Kernel Approximation on Compact Homogeneous Spaces
%U https://leicester.figshare.com/articles/Kernel_Approximation_on_Compact_Homogeneous_Spaces/10120043
%2 https://leicester.figshare.com/ndownloader/files/18237383
%K IR content
%X 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.