On the best $L_1$-approximations of functional classes by splines under restrictions imposed on their derivatives
We find the exact asymptotics ($n → ∞$) of the best $L_1$-approximations of classes $W_1^r$ of periodic functions by splines $s ∈ S_{2n, r∼-1}$ ($S_{2n, r∼-1}$ is a set of $2π$-periodic polynomial splines of order $r−1$, defect one, and with nodes at the points $kπ/n,\; k ∈ ℤ$) such that $V_0^{2π} s...
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| Дата: | 1999 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1999
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4629 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510777197199360 |
|---|---|
| author | Babenko, V. F. Parfinovych, N. V. Бабенко, В. Ф. Парфинович, Н. В. Бабенко, В. Ф. Парфинович, Н. В. |
| author_facet | Babenko, V. F. Parfinovych, N. V. Бабенко, В. Ф. Парфинович, Н. В. Бабенко, В. Ф. Парфинович, Н. В. |
| author_sort | Babenko, V. F. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:10:18Z |
| description | We find the exact asymptotics ($n → ∞$) of the best $L_1$-approximations of classes $W_1^r$ of periodic functions by splines $s ∈ S_{2n, r∼-1}$ ($S_{2n, r∼-1}$ is a set of $2π$-periodic polynomial splines of order $r−1$, defect one, and with nodes at the points $kπ/n,\; k ∈ ℤ$) such that $V_0^{2π} s^{( r-1)} ≤ 1+ɛ_n$, where $\{ɛ_n\}_{n=1}^{ ∞}$ is a decreasing sequence of positive numbers such that $ɛ_n n^2 → ∞$ and $ɛ_n → 0$ as $n → ∞$. |
| first_indexed | 2026-03-24T03:02:23Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4629 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:02:23Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/cd/ed41eac3ad1a5f5c0ad7ae9d3cf032cd.pdf |
| spelling | umjimathkievua-article-46292020-03-18T21:10:18Z On the best $L_1$-approximations of functional classes by splines under restrictions imposed on their derivatives О наилучших $L_1$-приближениях функциональных классов сплайнами при наличии ограничений на их производные Babenko, V. F. Parfinovych, N. V. Бабенко, В. Ф. Парфинович, Н. В. Бабенко, В. Ф. Парфинович, Н. В. We find the exact asymptotics ($n → ∞$) of the best $L_1$-approximations of classes $W_1^r$ of periodic functions by splines $s ∈ S_{2n, r∼-1}$ ($S_{2n, r∼-1}$ is a set of $2π$-periodic polynomial splines of order $r−1$, defect one, and with nodes at the points $kπ/n,\; k ∈ ℤ$) such that $V_0^{2π} s^{( r-1)} ≤ 1+ɛ_n$, where $\{ɛ_n\}_{n=1}^{ ∞}$ is a decreasing sequence of positive numbers such that $ɛ_n n^2 → ∞$ and $ɛ_n → 0$ as $n → ∞$. Знайдено точну асимптотику (при $n → ∞$) найкращих $L_1$ наближень класів $W_1^r$ періодичних функцій сплайнами $s ∈ S_{2n, r∼-1}$ ($S_{2n, r∼-1}$ —множина $2π$-періодичних поліноміальиих сплайнів порядку $r−1$, дефекту 1,з вузлами в точках $kπ/n,\; k ∈ ℤ$) такими, що $V_0^{2π} s^{( r-1)} ≤ 1+ɛ_n$ де $\{ɛ_n\}_{n=1}^{ ∞}$ — спадна послідовність додатних чисел така, що $ɛ_n n^2 → ∞$ і $ɛ_n → 0$, якщо $n → ∞$. Institute of Mathematics, NAS of Ukraine 1999-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4629 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 4 (1999); 435-444 Український математичний журнал; Том 51 № 4 (1999); 435-444 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4629/5961 https://umj.imath.kiev.ua/index.php/umj/article/view/4629/5962 Copyright (c) 1999 Babenko V. F.; Parfinovych N. V. |
| spellingShingle | Babenko, V. F. Parfinovych, N. V. Бабенко, В. Ф. Парфинович, Н. В. Бабенко, В. Ф. Парфинович, Н. В. On the best $L_1$-approximations of functional classes by splines under restrictions imposed on their derivatives |
| title | On the best $L_1$-approximations of functional classes by splines under restrictions imposed on their derivatives |
| title_alt | О наилучших $L_1$-приближениях функциональных
классов сплайнами при наличии ограничений на их производные |
| title_full | On the best $L_1$-approximations of functional classes by splines under restrictions imposed on their derivatives |
| title_fullStr | On the best $L_1$-approximations of functional classes by splines under restrictions imposed on their derivatives |
| title_full_unstemmed | On the best $L_1$-approximations of functional classes by splines under restrictions imposed on their derivatives |
| title_short | On the best $L_1$-approximations of functional classes by splines under restrictions imposed on their derivatives |
| title_sort | on the best $l_1$-approximations of functional classes by splines under restrictions imposed on their derivatives |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4629 |
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