Shape preserving approximation of periodic functions -- Conclusion
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917585604313088 |
|---|---|
| author | Leviatan, D. Shevchuk, I. O. |
| author_facet | Leviatan, D. Shevchuk, I. O. |
| contents | We give here the final results about the validity of Jackson-type estimates in comonotone approximation of $2π$-periodic functions by trigonometric polynomials. For coconvex and the so called co-$q$-monotone, $q>2$, approximations, everything is known by now. Thus, this paper concludes the research on Jackson type estimates of Shape Preserving Approximation of periodic functions by trigonometric polynomials. It is interesting to point out that the results for comonotone approximation of a periodic function are substantially different than the analogous results for comonotone approximation, by algebraic polynomials, of a continuous function on a finite interval. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shape preserving approximation of periodic functions -- Conclusion Leviatan, D. Shevchuk, I. O. Classical Analysis and ODEs 41A29, 42A10, 41A25 We give here the final results about the validity of Jackson-type estimates in comonotone approximation of $2π$-periodic functions by trigonometric polynomials. For coconvex and the so called co-$q$-monotone, $q>2$, approximations, everything is known by now. Thus, this paper concludes the research on Jackson type estimates of Shape Preserving Approximation of periodic functions by trigonometric polynomials. It is interesting to point out that the results for comonotone approximation of a periodic function are substantially different than the analogous results for comonotone approximation, by algebraic polynomials, of a continuous function on a finite interval. |
| title | Shape preserving approximation of periodic functions -- Conclusion |
| topic | Classical Analysis and ODEs 41A29, 42A10, 41A25 |
| url | https://arxiv.org/abs/2402.06103 |