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Tohoku Mathematical Journal
SECOND SERIES VOL. 61, NO. 4
|Tohoku Math. J.|
61 (2009), 571-588
THE LAPLACIAN AND THE HEAT KERNEL ACTING ON DIFFERENTIAL FORMS ON SPHERES
(Received December 22, 2008, revised July 9, 2009)
We show that the Laplacian acting on differential forms on a sphere can be lifted to an operator on its rotation group which is intrinsically equivalent to the Laplacian acting on functions on the Lie group. Further, using the result and the Urakawa summation formula for the heat kernel of the latter Laplacian and the Weyl integration formula, we get a summation formula for the kernel of the former.
2000 Mathematics Subject Classification.
Primary 58J35; Secondary 58J37.
Key words and phrases.
Sphere, Laplacian, heat kernel.
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