The Laplacian and the heat kernel acting on differential forms on spheres
Masayoshi Nagase
Source: Tohoku Math. J. (2) Volume 61, Number 4
(2009), 571-588.
Abstract
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.tmj/1264084500
Digital Object Identifier: doi:10.2748/tmj/1264084500
Zentralblatt MATH identifier: 05687944
Mathematical Reviews number (MathSciNet): MR2598250
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