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Higher Laplace–Beltrami Operators on Bounded Symmetric Domains

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Abstract

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 Kähler 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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Acknowledgements

We thank the referees for very helpful comments and suggestions on the Conjecture 1.2.

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Authors and Affiliations

  1. >Mathematics Institute, Žitná 25, 11567, Prague 1, Czech Republic

    Miroslav Engliš

  2. Mathematics Institute, Na Rybníčku 1, 74601, Opava, Czech Republic

    Miroslav Engliš

  3. Center of Mathematical Sciences, Zhejiang University, Zhejiang, 310027, P. R. China

    Hao Xu

Authors
  1. Miroslav Engliš
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  2. Hao Xu
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Corresponding author

Correspondence to Miroslav Engliš.

Additional information

In Memory of Professor Qikeng Lu (1927–2015)

M. E. was supported by GA CR (Grant No. 201/12/G028) and by RVO funding for IC (Grant No. 67985840)

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Engliš, M., Xu, H. Higher Laplace–Beltrami Operators on Bounded Symmetric Domains. Acta. Math. Sin.-English Ser. 34, 1297–1312 (2018). https://doi.org/10.1007/s10114-018-8162-y

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  • DOI: https://doi.org/10.1007/s10114-018-8162-y

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