Jackson – Stechkin-type inequalities for the approximation of elements of Hilbert spaces
We introduce new characteristics for elements of Hilbert spaces, namely, generalized moduli of continuity \$\omega_{ \varphi} (x, L_p, V ([0, \delta]))$ and obtain new exact Jackson – Stechkin-type inequalities with these moduli of continuity for the approximation of elements of Hilbert spaces. Thes...
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| Date: | 2018 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2018
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1626 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We introduce new characteristics for elements of Hilbert spaces, namely, generalized moduli of continuity \$\omega_{ \varphi} (x, L_p, V ([0, \delta]))$ and obtain new exact Jackson – Stechkin-type inequalities with these moduli of continuity for the approximation of
elements of Hilbert spaces. These results include numerous well-known inequalities for the approximation of periodic functions by trigonometric polynomials, approximation of nonperiodic functions by entire functions of exponential type, similar results for almost periodic functions, etc. Some of these results are new even in these classical cases. |
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