Geodesic
Laurent-Hua Loo-Keng series with respect to the matrix ball from space ${{\mathbb{C}}^{n}}\left[ m\times m \right]$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 5, pp. 589-598

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The aim of this work is to obtain multidimensional analogs of the Laurent series with respect to the matrix ball from space ${{\mathbb{C}}^{n}}\left[ m\times m \right]$. To do this, we first introduce the concept of a "layer of the matrix ball" from ${{\mathbb{C}}^{n}}\left[ m\times m \right]$, then in this layer of the matrix ball we use the properties of integrals of the Bochner-Hua Loo-Keng type to obtain analogs of the Laurent series.
Keywords: holomorphic function, Shilov's boundary, Bochner-Hua Loo Keng integral, orthonormal system.
Mots-clés : matrix ball, Laurent series 
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     author = {Gulmirza Kh. Khudayberganov and Jonibek Sh. Abdullayev},
     title = {Laurent-Hua {Loo-Keng} series with respect to the matrix ball from space ${{\mathbb{C}}^{n}}\left[ m\times m \right]$},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     publisher = {mathdoc},
     volume = {14},
     number = {5},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_5_a5/}
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Gulmirza Kh. Khudayberganov; Jonibek Sh. Abdullayev. Laurent-Hua Loo-Keng series with respect to the matrix ball from space ${{\mathbb{C}}^{n}}\left[ m\times m \right]$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 5, pp. 589-598. http://geodesic.mathdoc.fr/item/JSFU_2021_14_5_a5/