Heat Kernel for the Sub-Laplacian on the Sphere S3
This section deals with the study of the heat kernel of a sub-Laplacian on the three-dimensional sphere, and a Grushin-type operator on S2, called the spherical Grushin operator. This is a hypoelliptic operator on S2 and is defined by the method explained in the previous chapter. The method of investigation is the explicit determination of eigenvalues and eigenfunctions of the Laplacian and sub-Laplacian in terms of harmonic polynomials (see [97, 7, 8, 9]).
KeywordsHeat Kernel Volume Form Principal Symbol Harmonic Polynomial Complex Line Bundle
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