Geodesic
On volumes of matrix ball of third type and generalized Lie balls
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 29 (2019) no. 4, pp. 548-557
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The third-type matrix ball and the generalized Lie ball that are connected with classical domains play a crucial role in the theory of several complex variable functions. In this paper the volumes of the third type matrix ball and the generalized Lie ball are calculated. The full volumes of these domains are necessary for finding kernels of integral formulas for these domains (kernels of Bergman, Cauchy-Szegö, Poisson etc.). In addition, it is used for the integral representation of a function holomorphic on these domains, in the mean value theorem and other important concepts. The results obtained in this article are the general case of results of Hua Lo-ken and his results in particular cases coincides with our results.
Keywords: classical domains, matrix ball of the first type, matrix balls of the second type, matrix balls of the third type, generalized Lie ball. 
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U. S. Rakhmonov; J. Sh. Abdullayev. On volumes of matrix ball of third type and generalized Lie balls. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 29 (2019) no. 4, pp. 548-557. http://geodesic.mathdoc.fr/item/VUU_2019_29_4_a5/

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