Higher Laplace–Beltrami Operators on Bounded Symmetric Domains |
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基金项目: | GA CR (Grant No. 201/12/G028) and by RVO funding for IC (Grant No. 67985840) |
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摘 要: | It was conjectured by the first author and Peetre that the higher Laplace–Beltrami operators generate the whole ring of invariant operators on bounded symmetric domains. We give a proof of the conjecture for domains of rank ≤ 6 by using a graph manipulation of K¨ahler curvature tensor. We also compute higher order terms in the asymptotic expansions of the Bergman kernels and the Berezin transform on bounded symmetric domain.
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