Gulmirza Kh. Khudayberganov, Jonibek Sh. Abdullayev, “Relationship between the Bergman and Cauchy-Szegö in the domains $\tau ^{+}(n-1)$ и $\Re _{IV}^{n}$”, J. Sib. Fed. Univ. Math. Phys., 13:5 (2020), 559

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Journal of Siberian Federal University. Mathematics & Physics, 2020, Volume 13, Issue 5, Pages 559–567
DOI: https://doi.org/10.17516/1997-1397-2020-13-5-559-567 (Mi jsfu862)

This article is cited in 7 scientific papers (total in 7 papers)

Relationship between the Bergman and Cauchy-Szegö in the domains

$\tau ^{+}(n-1)$ и

$\Re _{IV}^{n}$

Gulmirza Kh. Khudayberganov, Jonibek Sh. Abdullayev

National University of Uzbekistan, Tashkent, Uzbekistan

Full-text PDF (136 kB) Citations (7)

References:

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DOI: https://doi.org/10.17516/1997-1397-2020-13-5-559-567

Abstract: In this paper, a connection has been established between the Bergman and Cauchy-Szegö kernels using the biholomorphic equivalence of the domains

$\tau ^{+} \left(n-1\right)$ and the Lie ball

$\Re _{IV}^{n}$ . Moreover, integral representations of holomorphic functions in these domains are obtained.

Keywords: classical domains, Lie ball, future tube, Shilov's boundary, Jacobian, Bergman's kernel, Cauchy-Szegö's kernel, Poisson's kernel.

Funding agency	Grant number
Academy of Sciences of the Republic of Uzbekistan	OT-F4-37 OT-F4-29
Ministry of Innovative Development of the Republic of Uzbekistan
OT-F4-(37+29) Functional properties of $A$ -analytical functions and their applications. Some problems of complex analysis in matrix domains (2017--2021 y.) Ministry of Innovative Development of the Republic of Uzbekistan.

Received: 02.05.2020
Received in revised form: 30.05.2020
Accepted: 08.07.2020

Bibliographic databases:

Document Type: Article

UDC: 517.55

Language: English

Citation: Gulmirza Kh. Khudayberganov, Jonibek Sh. Abdullayev, “Relationship between the Bergman and Cauchy-Szegö in the domains

$\tau ^{+}(n-1)$ и

$\Re _{IV}^{n}$ ”, J. Sib. Fed. Univ. Math. Phys., 13:5 (2020), 559–567

Citation in format AMSBIB

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\by Gulmirza~Kh.~Khudayberganov, Jonibek~Sh.~Abdullayev

\paper Relationship between the Bergman and Cauchy-Szeg\"{o} in the domains  $\tau ^{+}(n-1)$ и $\Re _{IV}^{n}$

\jour J. Sib. Fed. Univ. Math. Phys.

\yr 2020

\vol 13

\issue 5

\pages 559--567

\mathnet{http://mi.mathnet.ru/jsfu862}

\crossref{https://doi.org/10.17516/1997-1397-2020-13-5-559-567}

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Linking options:

https://www.mathnet.ru/eng/jsfu862

https://www.mathnet.ru/eng/jsfu/v13/i5/p559

This publication is cited in the following 7 articles:

Gulmirza Kh. Khudaiberganov, Kutlimurot S. Erkinboev, “Some properties of the automorphisms of the classical domain of the first type in the space $\mathbb{C}\left[ m\times n \right]$”, Zhurn. SFU. Ser. Matem. i fiz., 17:3 (2024), 295–303
Uktam S. Rakhmonov, Jonibek Sh. Abdullayev, “On properties of the second type matrix ball $B_{m,n}^{(2)}$ from space ${\mathbb C}^{n}[m\times m]$”, Zhurn. SFU. Ser. Matem. i fiz., 15:3 (2022), 329–342
U. S. Rakhmonov, Z. K. Matyakubov, “Carleman's formula for the matrix domains of Siegel”, Chebyshevskii sb., 23:4 (2022), 126–135
G. Khudayberganov, J. Sh. Abdullayev, “Holomorphic continuation into a matrix ball of functions defined on a piece of its skeleton”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:2 (2021), 296–310
Gulmirza Kh. Khudayberganov, Jonibek Sh. Abdullayev, “Laurent-Hua Loo-Keng series with respect to the matrix ball from space ${{\mathbb{C}}^{n}}\left[ m\times m \right]$”, Zhurn. SFU. Ser. Matem. i fiz., 14:5 (2021), 589–598
J. Sh. Abdullayev, “Estimates the Bergman kernel for classical domains É. Cartan's”, Chebyshevskii sb., 22:3 (2021), 20–31
Jonibek Sh. Abdullayev, “An analogue of Bremermann's theorem on finding the Bergman kernel for the Cartesian product of the classical domains ${{\Re }_{I}}\left( m,k \right)$ and ${{\Re }_{II}}\left( n \right)$”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 3, 88–96

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Журнал Сибирского федерального университета. Серия "Математика и физика"

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