On the Transmission of the Approximate Properties from I_ρ(f;x) to the Corresponding I(f;x;ρ)

Abstract:

      In this paper, the multiplicator method, which was introduced by the author, is applied to research the transmission of the approximate properties from I_ρ(f;x) to the corresponding I(f;x;ρ). As a result, the indirect theorems, inverse theorems and asymptotic expansions of Fejér-Коровкйн and Ghermanesco non-periodic singular convolution integrals are derived.