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Journal of Siberian Federal University. Mathematics & Physics, 2025, Volume 18, Issue 4, Pages 484–490 (Mi jsfu1263)  
On Carleman's formula in ${{\mathbb{C}}^{n}}\left[ m\times m \right]$

Gulmirza Khudayberganova, Barlikbay B. Prenovb, Jonibek Sh. Abdullayevc, Kudrat Sh. Ruzmetovd

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
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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.
Received: 12.10.2024
Received in revised form: 09.12.2024
Accepted: 24.03.2025
Bibliographic databases:
Document Type: Article
UDC: 517.953
Language: English
Citation: Gulmirza Khudayberganov, Barlikbay B. Prenov, Jonibek Sh. Abdullayev, Kudrat Sh. Ruzmetov, “On Carleman's formula in ${{\mathbb{C}}^{n}}\left[ m\times m \right]$”, J. Sib. Fed. Univ. Math. Phys., 18:4 (2025), 484–490
Citation in format AMSBIB
\Bibitem{KhuPreAbd25}
\by Gulmirza~Khudayberganov, Barlikbay~B.~Prenov, Jonibek~Sh.~Abdullayev, Kudrat~Sh.~Ruzmetov
\paper On Carleman's formula in ${{\mathbb{C}}^{n}}\left[ m\times m \right]$
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2025
\vol 18
\issue 4
\pages 484--490
\mathnet{http://mi.mathnet.ru/jsfu1263}
\edn{https://elibrary.ru/JFMMFC}
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    		Журнал Сибирского федерального университета. Серия "Математика и физика"
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