On N-Widths of Holomorphic-Functions of Several Variables Original Research Article

We consider the classes of holomorphic functions whose radial derivative of order r lies in the unit ball of the Hardy space H2(Bn) or the Bergman space A2(Bn). For these classes we calculate the linear and Gel′fand N-widths in C(Sρ), where Sρ is the sphere in Cn of radius 0 < ρ < 1. Some results are obtained for analogous problems in polydiscs and for 2π-periodic functions of one variable holomorphic in a strip.