Abstract
For the perturbed Bergman Laplacians Δαβ given by in the unit ball B n of C n we establish explicit formulae for the corresponding wave equations in B n. The formulae obtained generalise, for arbitrary αβε, the formulae given in [2] and [5] for the wave equation associated to the shifted Bergman Laplacian Δα=Δ00 in B n. Moreover, using an analytic continuation argument, we are able to give explicit formulae for the solutions of the wave equation associated to a two parameter family of Laplacians Δα,α on C n which are natural deformations of the Fubini-Study Laplacian on the Projective space P n(C) , n ≥1, viewed as the dual space of the Bergman ball B n.
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Intissar, A., Ould Moustapha, M.V. Explicit Formulae for the Wave Kernels for the Laplacians Δαβ in the Bergman Ball Bn,n≥1. Annals of Global Analysis and Geometry 15, 221–234 (1997). https://doi.org/10.1023/A:1006501627929
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DOI: https://doi.org/10.1023/A:1006501627929