The paper studies the region of values Dm,n(T) of the system {f(z1), f(z2),..., f(zm), f(r1), f(r2),..., f(rn)}, where m ≥ 1; n > 1; z j, j = 1, ... m, are arbitrary fixed points of the disk U = {z: |z| < 1} with Im zj ≠ 0, j = 1, 2, ..., m; rj, 0 < rj < 1, j = 1, 2, ..., n, are fixed; f T, and the class T consists of functions f(z) = z + c2z2 + ... regular in the disk U and satisfying the condition Im f(z) • Im z > 0 for Im z ≠= 0, z ∈ U. An algebraic characterization of the set Dm,n(T) in terms of nonnegative-definite Hermitian forms is provided, and all the boundary functions are described. As an implication, the region of values of f(z 1) in the subclass of functions f T with prescribed values f(r j) (j = 1, 2, 3) is determined. Bibliography: 12 titles. © Springer Science+Business Media, Inc. 2007.
