Approximation of classes of Poisson integrals by rectangular Fejér means - Rovenska, Olga (Frontiers in Applied Mathematics and Statistics, 2024)
The article is devoted to the problem of approximation of classes of periodic functions by rectangular linear means of Fourier series. Asymptotic equalities are found for upper bounds of deviations in the uniform metric of rectangular Fej ér means on classes of periodic functions of several variables generated by sequences that tend to zero at the rate of geometric progression.In one-dimensional case, these classes consist of Poisson integrals, namely functions that can be regularly extended in the fixed strip of complex plane.