Higher Laplace-Beltrami Operators on Bounded Symmetric Domains

@article{30222,
   author = {Engliš, Miroslav and Xu, Hao},
   article_location = {Heidelberg},
   article_number = {8},
   doi = {http://dx.doi.org/10.1007/s10114-018-8162-y},
   keywords = {Higher Laplace-Beltrami operators; bounded symmetric domains; Bergman Kernel},
   language = {eng},
   issn = {1439-8516},
   journal = {Acta Mathematica Sinica, English Series},
   title = {Higher Laplace-Beltrami Operators on Bounded Symmetric Domains},
   url = {https://link.springer.com/article/10.1007%2Fs10114-018-8162-y},
   volume = {34},
   year = {2018}
}

TY  - JOUR
ID  - 30222
AU  - Engliš, Miroslav - Xu, Hao
PY  - 2018
TI  - Higher Laplace-Beltrami Operators on Bounded Symmetric Domains
JF  - Acta Mathematica Sinica, English Series
VL  - 34
IS  - 8
SP  - 1297-1312
EP  - 1297-1312
PB  - Springer Verlag
SN  - 14398516
KW  - Higher Laplace-Beltrami operators
KW  - bounded symmetric domains
KW  - Bergman Kernel
UR  - https://link.springer.com/article/10.1007%2Fs10114-018-8162-y
L2  - https://link.springer.com/article/10.1007%2Fs10114-018-8162-y
N2  - 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 Kahler curvature tensor. We also compute higher order terms in the asymptotic expansions of the Bergman kernels and the Berezin transform on bounded symmetric domain.
ER  - 

ENGLIŠ, Miroslav and Hao XU. Higher Laplace-Beltrami Operators on Bounded Symmetric Domains. \textit{Acta Mathematica Sinica, English Series}. Heidelberg: Springer Verlag, 2018, vol.~34, No~8, p.~1297-1312. ISSN~1439-8516. Available from: https://dx.doi.org/10.1007/s10114-018-8162-y.