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In the paper we construct a counterpart of classical results on the generalized (l, d)equiangular system points on the rays in the case of arbitrary multidimensional complex spaces. Introduction This paper belongs to the theory of extremal problems on classes of non-overlapping domain, in the case of arbitrary multidimensional complex spaces. The begin of these investigations associated, in space C, with the paper of M.A. Lavrent’ev [1] in 1934. He found the maximum of some functional with respect to two simply connected domains with two fixed points. We note that this result was needed him for applying to some aerodynamics problems. In 1947, G.M. Goluzin solved a similar problem for three fixed points on the complex plane [2]. Then the topic began to evolve rapidly. In this connection we may recall papers of many authors, including Y.E. Alenitsina, M.A. Lebedev, J. Jenkins, P.M. Tamrazov, P.P. Kufareva and others. Using the idea of P.M. Tamrazov, in 1975 G.P. Bakhtin solved first the problem with so-called ”free poles” on the unit circle, see, e.g., [3]. An important step for the development of this topic was papers of V.N. Dubinin. He developed a new method of research that is method of piecewise-separating transformation. He also first solved numerous of extremal problems for an arbitrary but fixed multiconnected non-overlapping domains (see, e.g., [4], [5], [6]). Now this type of extremal problems is used for investigations in holomorphic dynamics. In the last decade actively used Bakhtin’s method of ”managing functional”. He managed to solve a series of extremal problems for so-called ”radial systems of points” (see, e.g., [4], [7]–[13]). In the space C, n ≥ 2, the first results were obtained in [14]–[16]. In the present paper, we use these results.

Extremal Problems on the Generalized (<i>l, d</i>)-Equiangular System Points in the Case of Arbitrary Multidimensional Complex Spaces