Best orthogonal trigonometric approximations of the Nikol'skii-Besov-type classes of periodic functions of one and several variables

Authors

  • O.V. Fedunyk-Yaremchuk Lesya Ukrainka Eastern European National University, 9 Potapova str., 43025, Lutsk, Ukraine
  • S.B. Hembars'ka Lesya Ukrainka Eastern European National University, 9 Potapova str., 43025, Lutsk, Ukraine
https://doi.org/10.15330/cmp.14.1.171-184

Keywords:

Nikol'skii-Besov-type class, step hyperbolic Fourier sum, best orthogonal trigonometric approximation, orthowidth
Published online: 2022-06-22

Abstract

We obtained the exact order estimates of the best orthogonal trigonometric approximations of periodic functions of one and several variables from the Nikol'skii-Besov-type classes B1,θω (B1,θΩ in the multivariate case d2) in the space B,1. We observe that in the multivariate case the orders of mentioned approximation characteristics of the functional classes B1,θΩ are realized by their approximations by step hyperbolic Fourier sums that contain the necessary number of harmonics. In the univariate case, an optimal in the sense of order estimates for the best orthogonal trigonometric approximations of the corresponding functional classes are the ordinary partial sums of their Fourier series. As a consequence of the obtained results, the exact order estimates of the orthowidths of the classes B1,θω (B1,θΩ for d2) in the space B,1 are also established. Besides, we note that in the univariate case, in contrast to the multivariate one, the estimates of the considered approximation characteristics do not depend on the parameter θ.

How to Cite
(1)
Fedunyk-Yaremchuk, O.; Hembars'ka, S. Best Orthogonal Trigonometric Approximations of the Nikol’skii-Besov-Type Classes of Periodic Functions of One and Several Variables. Carpathian Math. Publ. 2022, 14, 171-184.

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