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J. Sib. Fed. Univ. Math. Phys., 2020, Volume 13, Issue 5, Pages 559–567 (Mi jsfu862)  

This article is cited in 1 scientific paper (total in 1 paper)

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

Abstract: In this paper, a connection has been established between the Bergman and Cauchy-Szegö kernels using the biholomorphic equivalence of the domains $\tau ^{+} (n-1)$ 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.


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

Full text: PDF file (136 kB)
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Bibliographic databases:

UDC: 517.55
Received: 02.05.2020
Received in revised form: 30.05.2020
Accepted: 08.07.2020
Language:

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
\Bibitem{KhuAbd20}
\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}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000580315300004}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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