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| The Heat Kernel of a Ball in C^n |
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Citation： |
Lu Qikeng(陆启铿).The Heat Kernel of a Ball in C^n[J].Chinese Annals of Mathematics B,1990,11(1):1~14 |
| Page view： 763
Net amount： 882 |
Authors： |
Lu Qikeng(陆启铿); |
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| Abstract： |
By introducing the horosphere coordinate of a unit ball B^n in C^n and an integral transformation formula of functions in such coordidates, the author constructs the heat kernel H_B^n(z,w,t) of the heat equation associated to the Bergman metric of B^n.That is
$H_B^n(z,w,t)=c_n(-1/\pi)^ne^{-n^2t}/\sqrt(t)\int_-\infty^\infty{[1/sh2\sigma\partial/\partial\sigma(1/sh\sigma\partial/\partial)^n-1e^{-\sigma^2/4t}]_{ch2\sigma=ch2r(x,w)+\tau^2}d\tau$
where c_n is a well-defined constant and r(z, w) is the geodesic destanco of two points s and w of B^n and t\in R^+. Since
$H_B^m*B^n=H_B^m\cdot H_B^n$
then
$G((z_1,z_2),(w_1,w_2))=-\int_0^\infty{H_B^m(z_1,w_1,t)H_B^n(z_2,w_2,t)}dt$
is the Green function of the topological product space B^m*B^n. |
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