Gulmirza Khudayberganov, Barlikbay B. Prenov, Jonibek Sh. Abdullayev, Kudrat Sh. Ruzmetov, “On Carleman's formula in <nobr>${{\mathbb{C}}^{n}}\left[ m\times m \right]$</nobr>”, J. Sib. Fed. Univ. Math. Phys., 2025, Volume 18, Issue 4,Pages <nobr>484

On Carleman's formula in ${{\mathbb{C}}^{n}}\left[ m\times m \right]$

Gulmirza Khudayberganov^a, Barlikbay B. Prenov^b, Jonibek Sh. Abdullayev^c, Kudrat Sh. Ruzmetov^d

^a National University of Uzbekistan, Tashkent, Uzbekistan
^b Nukus state pedagogical institute named after Ajiniyaz, Nukus, Republic of Karakalpakstan, Uzbekistan
^c Urgench State University, Urgench, Uzbekistan
^d Tashkent State Agrarian University, Tashkent, Uzbekistan

Abstract: This paper considers Carleman's integral formula for a function of matrices in the space ${{\mathbb{C}}^{n}}\left[ m\times m \right]$. The resulting formula is a general case of G. Khudayberganov’s result.

Keywords: Carleman‘s formulas, holomorphic function, Hardy space, holomorphic continuation, matrix unit disc, automorphism.

UDC: 517.953

Received: 12.10.2024
Received in revised form: 09.12.2024
Accepted: 24.03.2025

Language: English