Silin Y. Approximation by the Valle-Poussin's operators of functions given on the real line

The thesis contains the researches on the problems of approximation by Valle-Poussin's operators on the classes of functions, which locally summable on the real line and determined by psi-integrals, and the researches of simultaneous approximation of some functions of this classes. We find asymptotic formulas of deviations of the Valle-Poussin's operators on the some classes and under some natural limits of parameters, defining the classes and method of approximation provide solution of the corresponding problem of Kolmogorov-Nikol'skii. The cases have been considered in thesis when the classes are defined by slowly going downward and quickly going downword to zero functions psi . We obtain asymptotic laws of decreasing of functionals which characterize the problem of simultaneous approximation of psi -integrals of continuous functions by the Valle-Poussin's operators in the uniform metric