Estimates of the best bilinear approximations for the classes of $(ψ,β)$-differentiable periodic multivariate functions
Order estimates are obtained for the best bilinear approximations of $2d$-variable functions $f(x y),\; x, y \in \pi_d,\; \pi_d =\prod^d_{j=1} [ \pi , \pi ]$, formed by $d$-variable functions $f(x) \in L^{\psi}_{\beta} ,p$ by the shifts of their argument $x \in \pi_d$ by all possible values of $y...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2018
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1576 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | Order estimates are obtained for the best bilinear approximations of $2d$-variable functions $f(x y),\;
x, y \in \pi_d,\; \pi_d =\prod^d_{j=1} [ \pi , \pi ]$, formed by $d$-variable functions $f(x) \in L^{\psi}_{\beta} ,p$ by the shifts of their argument $x \in \pi_d$ by all possible
values of $y \in \pi_d$ in the space $L_{q_1,q_2} (\pi 2d)$. The results include various relations between the parameters $p, q_1$ and $q_2$. |
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