Direct and inverse approximation theorems in Banach spaces and Fourier transforms

An author's summary of a thesis submitted for the degree of Doctor of Physico-Mathematical Sciences. The dissertation was defended December 19, 1969, at a session of the scientific council of the Mechanical-Mathematics Faculty of the M. V. Lomonosov Moscow State University. The official opponents were Professors V. K. Dzyadyk, B. M. Levitan, and S. B. Stechkin, all Doctors of physico-mathematical sciences.Translated from Matematicheskie Zametki, Vol. 7, No. 6, pp. 765–778, June, 1970.