Geodesic
Estimates the Bergman kernel for classical domains \'{E}.~Cartan's
Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 20-31

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The aim of this work is to find optimal estimates for the Bergman kernels for the classical domains ${{\Re }_{I}}\left( m,k \right),{{\Re }_{II}}\left( m \right),{{\Re }_{III}}\left( m \right)$ and ${{\Re }_{IV}}\left( n \right)$ through the Bergman kernels of balls in the spaces ${{\mathbb{C}}^{mk}},{{\mathbb{C}}^{\frac{m\left( m+1 \right)}{2}}},{{\mathbb{C}}^{\frac{m\left( m-1 \right)}{2}}}$ and ${{\mathbb{C}}^{n}}$, respectively. For this, we use the statements of the Summer-Mehring theorem on the extension of the Bergman kernel and some properties of the Bergman kernel.
Keywords: classical domains, Bergman's kernel, homogeneous domain, symmetric domain, orthonormal system. 
@article{CHEB_2021_22_3_a2,
     author = {J. Sh. Abdullayev},
     title = {Estimates the {Bergman} kernel for classical domains {\'{E}.~Cartan's}},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {20--31},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a2/}
}
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J. Sh. Abdullayev. Estimates the Bergman kernel for classical domains \'{E}.~Cartan's. Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 20-31. http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a2/