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., 2020, Volume 13, Issue 5,Pages 559

This article is cited in 8 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

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.

UDC: 517.55

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

Language: English

DOI: 10.17516/1997-1397-2020-13-5-559-567