Laurent-Hua Loo-Keng series with respect to the matrix ball from space ${{\mathbb{C}}^{n}}\left[ m\times m \right]$

Gulmirza Kh. Khudayberganov ; Jonibek Sh. Abdullayev

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 5, pp. 589-598.

Résumé

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.

Détail

Keywords: holomorphic function, Shilov's boundary, Bochner-Hua Loo Keng integral, orthonormal system.
Mots-clés : matrix ball, Laurent series

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