Обобщенные сдвиги Бесселя и некоторые обратные теоремы теории приближения функций на полупрямой

The generalized translations of Bessel and the harmonic analysis of Bessel may be used for study some problems of approximations of functions on the half-line $[0, +\infty)$ in the weighted $L_p$ spaces. Using generalized translations of Bessel we can define generalized moduli of continuity and we can consider many natural analogs of classical problems of approximation. As aggregates of approximation we use certain class of entire functions of exponential type. In this paper we obtain some analogs of classical inverse approximation theorems due to S. B. Stechkin, A. F. Timan and M. F. Timan.