Permutations and piecewise-constant approximation of continuous functions of n variables
We consider the problem of approximation of a continuous function f given on an n-dirnensional cube by step functions in the metrics of C and L p. We obtain exact error estimates in terms of the modulus of continuity of the function f or a special permutation of it.
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| Datum: | 1998 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1998
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4871 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511053757022208 |
|---|---|
| author | Korneichuk, N. P. Корнейчук, Н. П. Корнейчук, Н. П. |
| author_facet | Korneichuk, N. P. Корнейчук, Н. П. Корнейчук, Н. П. |
| author_sort | Korneichuk, N. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:16:14Z |
| description | We consider the problem of approximation of a continuous function f given on an n-dirnensional cube by step functions in the metrics of C and L p. We obtain exact error estimates in terms of the modulus of continuity of the function f or a special permutation of it. |
| first_indexed | 2026-03-24T03:06:47Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4871 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:06:47Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/7a/74403da17b4142e235de149acb47617a.pdf |
| spelling | umjimathkievua-article-48712020-03-18T21:16:14Z Permutations and piecewise-constant approximation of continuous functions of n variables Перестановки и кусочно-постоянное приближение непрерывных функций $n$ переменных Korneichuk, N. P. Корнейчук, Н. П. Корнейчук, Н. П. We consider the problem of approximation of a continuous function f given on an n-dirnensional cube by step functions in the metrics of C and L p. We obtain exact error estimates in terms of the modulus of continuity of the function f or a special permutation of it. Розглянуто задачу про наближення в метриках $C$ і $L_p$ заданої на $n$-вимірпому кубі неперервної функції $f$ ступінчастими функціями. Отримано точні оцінки похибки через модуль неперервності функції $f$ або її спеціальної перестановки. Institute of Mathematics, NAS of Ukraine 1998-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4871 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 7 (1998); 907–918 Український математичний журнал; Том 50 № 7 (1998); 907–918 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4871/6441 https://umj.imath.kiev.ua/index.php/umj/article/view/4871/6442 Copyright (c) 1998 Korneichuk N. P. |
| spellingShingle | Korneichuk, N. P. Корнейчук, Н. П. Корнейчук, Н. П. Permutations and piecewise-constant approximation of continuous functions of n variables |
| title | Permutations and piecewise-constant approximation of continuous functions of n variables |
| title_alt | Перестановки и кусочно-постоянное приближение непрерывных функций $n$ переменных |
| title_full | Permutations and piecewise-constant approximation of continuous functions of n variables |
| title_fullStr | Permutations and piecewise-constant approximation of continuous functions of n variables |
| title_full_unstemmed | Permutations and piecewise-constant approximation of continuous functions of n variables |
| title_short | Permutations and piecewise-constant approximation of continuous functions of n variables |
| title_sort | permutations and piecewise-constant approximation of continuous functions of n variables |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4871 |
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