An analogue of Bremermann’s theorem on finding the Bergman kernel for the Cartesian product of the classical domains ℜI (m, k) and ℜII (n)
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2023-12-18 09:49
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ABDULLAYEV, Jonibek Sh.. An analogue of Bremermann’s theorem on finding the Bergman kernel for the Cartesian product of the classical domains ℜI (m, k) and ℜII (n). In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2020, nr. 3(94), pp. 88-96. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 3(94) / 2020 / ISSN 1024-7696 /ISSNe 2587-4322

An analogue of Bremermann’s theorem on finding the Bergman kernel for the Cartesian product of the classical domains ℜI (m, k) and ℜII (n)

CZU: 517
MSC 2010: 26B10, 30C40, 32A25, 32N15, 58C10.

Pag. 88-96

Abdullayev Jonibek Sh.
 
National University of Uzbekistan named after Mirzo Ulugbek
 
 
Disponibil în IBN: 24 august 2021


Rezumat

In this paper, an analogue of Bremermann’s theorem on finding the Bergman kernel is obtained for the Cartesian product of classical domains. For this purpose, the groups of automorphisms of the considered domains are used, i.e., the Bergman kernels are constructed for the Cartesian product of classical domains, without applying complete orthonormal systems.

Cuvinte-cheie
Bergman’s kernel, classical domains, homogeneous domain, symmetric domain, Jacobian, orthonormal system