Integral representation of the sub-elliptic heat kernel on the complex anti-de Sitter fibration
We derive an integral representation for the subelliptic heat kernel of the complex anti-de Sitter fibration. Our proof is different from the one used in Wang (Potential Anal 45:635–653, 2016) since it appeals to the commutativity of the D’Alembertian and of the Laplacian acting on the vertical variable rather than the analytic continuation of the heat semigroup of the real hyperbolic space. Our approach also sheds the light on the connection between the sub-Laplacian of the above fibration and the so-called generalized Maass Laplacian, and on the role played by the odd dimensional real hyperbolic space.
KeywordsAnti-de Sitter fibration Hyperbolic ball Real hyperbolic space Subelliptic heat kernel Generalized Maass Laplacian
Mathematics Subject Classification35H20 35K08
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- 16.Ould Moustapha, M.V.: Heat kernel bounds on complex hyperbolic spaces. UnpublishedGoogle Scholar