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

National University of Uzbekistan, Tashkent, Uzbekistan

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

UDC: 517.55

Received: 10.08.2020
Received in revised form: 10.09.2020
Accepted: 20.10.2020

Language: English

DOI: 10.17516/1997-1397-2021-14-5-589-598

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