The best approximations and widths of the classes of periodical functions of one and several variables in the space B∞,1
Journal Title: Математичні Студії - Year 2019, Vol 51, Issue 1
Abstract
We obtained exact-order estimates of the best approximations of classes BΩ∞,θ of periodic functions of many variables and for classes Bωp,θ,1≤p≤∞ of functions of one variable by trigonometric polynomials with corresponding spectra of harmonics in the metric of space B∞,1. We also found exact orders for the Kolmogorov, linear and trigonometric widths of the same classes in space B∞,1.
Authors and Affiliations
M. V. Hembarskyi, S. B. Hembarska, K. V. Solich
Keywords
Related Articles
- EP ID EP584902
- DOI 10.15330/ms.51.1.74-85
- Views 59
- Downloads 0
Klein vs Mehrtens: restoring the reputation of a great modern
Historian Herbert Mehrtens sought to portray the history of turn-of-the-century mathematics as a struggle of modern vs countermodern, led respectively by David Hilbert and Felix Klein. Some of Mehrtens' conclusions have...
On removable singularities of mappings in uniform spaces
The paper is devoted to the study of mappings of two metric spaces that distort the modulus of families of paths by analogy with the Poletskii inequality.We deal with the situation when the mapping acts in a space that a...
The regularity of quotient paratopological groups
Let H be a closed subgroup of a regular Abelian paratopological group G. The group reflexion G♭ of G is the group G endowed with the strongest group topology, which is weaker than the original topology of G. We show that...
Fast growing meromorphic solutions of the systems of linear differential equations
Systems of linear differential equations that allow for dimension decrease are considered. Growth estimates for meromorphic vector-solutions are obtained. An essentially new feature is that there are no additional constr...
Geometric relations in an arbitrary metric space
The paper is devoted to individual elements of metric geometry. Analytical relations are considered that concern the distances between points of a metric space and have a definite geometric interpretation. These relation...