Гармонический анализ Данкля и некоторые задачи теории приближений функций. I

Some problems of aproximations of functions on the real line $\mathbb{R}$ in the $L_{2}$-metric with certain weight by entire functions of exponential growth are studied. Modules of continuity which used in problems are constructed with help of generalized translations of Dunkl. Direct theorems of Jacson type are proved.