QUALITATIVE ANALYSIS OF EXTREMAL PROBLEMS IN ARBITRARY DOMAINS

The author explores linear extremal problems of classes of bounded analytic functions and generalized classes discovered by V.I. Smirnov; the author also considers the representability of extremals by means of Cauchy-Stieltjes integral. The author considers the problems concerning where B is either a unit sphere in the (D) space or one of the classes , p>1. He shows the possibility of the results concerning the characteristic of extreme functions, their uniqueness, the possilble presentation of the functions from the classes and with the use of the Cauchy-Stieltjes integrals in the component of the D\ suppµ set and the boundary behavior of an extreme function from the (D) class. One should note that the given mathematical system can be implemented for making decisions in the field of construction engineering and structural analysis, it can provide research assistants and engineers with the background necessary for developing sound solutions and rational proposals