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Supported by the Austrian Federal Ministry of Education, Science and Culture

By Albert Boggess and Andrew RaichAlbert Boggess and Andrew Raich


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 ⊂ C n × C m. As a consequence, we can also compute the heat kernel associated to the weighted ∂-equation in C n when the weight is given by exp(−φ(z,z) ·λ) where φ: C n ×C n → C m is a quadratic, sesquilinear form and λ ∈ R m. Our method involves the representation theory of the Lie group M and the group Fourier transform. 1

Year: 2011
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