Abstract: | We give the algebraic characteristics of the range of the system Cp, C2p, ..., cnp f( ) ( fixed, 0<¦ ¦<1, n 1, P=1, 2, ...) on certain subclasses Cm,p, of the class C of functions, regular in the circle ¦z¦<1 and satisfying in it the condition Re f(z)>0. As an application one finds the range of f( ) on the subclasses C
m,p,
(n)
of functions from Cm,p, with prescribed coefficients cp c2p, ..., cnp.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 100, pp. 17–25, 1980. |