Abstract
In this article, we give an explicit calculation of the partial Fourier transform of the fundamental solution to the □ b -heat equation on quadric submanifolds M⊂ℂn×ℂm. As a consequence, we can also compute the heat kernel associated with the weighted \(\overline{\partial}\)-equation in ℂn when the weight is given by exp (−φ(z,z)⋅λ) where φ:ℂn×ℂn→ℂm is a quadratic, sesquilinear form and λ∈ℝm. Our method involves the representation theory of the Lie group M and the group Fourier transform.
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Communicated by Steve Bell.
The second author is partially funded by NSF grant DMS-0855822.
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Boggess, A., Raich, A. The □ b -Heat Equation on Quadric Manifolds. J Geom Anal 21, 256–275 (2011). https://doi.org/10.1007/s12220-010-9146-z
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DOI: https://doi.org/10.1007/s12220-010-9146-z