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- W108547227 abstract "In this thesis we establish an upper bound for the spherical heat kernel on the N-dimensionalunit sphere SN for N = 1; 2; 3. The strategy is to use the fact that the spherical heat kernel iscompletely determined by the ultraspherical heat kernel. By techniques from Fourier analysis,explicit formulas for the ultraspherical heat kernel with parameter = 1=2; 1=2 are deduced.Also, an integral formula for the kernel with parameter = 0 is introduced. By estimatingthese formulas for the ultraspherical heat kernels, the estimates of the spherical heat kernel areobtained.Furthermore, we prove that the periodized Gauss-Weierstrass kernel is strictly decreasingon [0; ]. Both an analytic and a probabilistic proof are given. A generalization of this resultis also established for small t, saying that the spherical heat kernel on S2 and S3 is strictlydecreasing as a function of the spherical distance between its two arguments." @default.
- W108547227 created "2016-06-24" @default.
- W108547227 creator A5028212939 @default.
- W108547227 date "2013-01-01" @default.
- W108547227 modified "2023-09-23" @default.
- W108547227 title "Estimates of the spherical and ultraspherical heat kernel" @default.
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