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Polynomial approximation on polytopes /
Polynomial approximation on convex polytopes in \mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the modu...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
[2014]
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1091. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
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| 008 | 140912t20142014riua ob 000 0 eng d | ||
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| 019 | |a 1259211690 |a 1262669170 | ||
| 020 | |a 9781470418946 |q (online) | ||
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| 035 | |a (OCoLC)890464618 |z (OCoLC)1259211690 |z (OCoLC)1262669170 | ||
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| 082 | 0 | 4 | |a 516/.158 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Totik, V., |e author. | |
| 245 | 1 | 0 | |a Polynomial approximation on polytopes / |c Vilmos Totik. |
| 264 | 1 | |a Providence, Rhode Island : |b American Mathematical Society, |c [2014] | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (v, 112 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v volume 232, number 1091 | |
| 500 | |a "Volume 232, Number 1091 (third of 6 numbers), November 2014." | ||
| 504 | |a Includes bibliographical references (pages 111-112). | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | 0 | |t Chapter 1. The result |t Chapter 2. Outline of the proof |t Chapter 3. Fast decreasing polynomials |t Chapter 4. Approximation on simple polytopes |t Chapter 5. Polynomial approximants on rhombi |t Chapter 6. Pyramids and local moduli on them |t Chapter 7. Local approximation on the sets $K_a$ |t Chapter 8. Global approximation of $F=F_n$ on $S_{1/32}$ excluding a neighborhood of the apex |t Chapter 9. Global approximation of $f$ on $S_{1/64}$ |t Chapter 10. Completion of the proof of Theorem 1.1 |t Chapter 11. Approximation in ${\mathbf R}^d$ |t Chapter 12. A $K$-functional and the equivalence theorem |t Chapter 13. The $L^p$ result |t Chapter 14. Proof of the $L^p$ result |t Chapter 15. The dyadic decomposition |t Chapter 16. Some properties of $L^p$ moduli of smoothness |t Chapter 17. Local $L^p$ moduli of smoothness |t Chapter 18. Local approximation |t Chapter 19. Global $L^p$ approximation excluding a neighborhood of the apex |t Chapter 20. Strong direct and converse inequalities |t Chapter 21. The $K$-functional in $L^p$ and the equivalence theorem. |
| 520 | |a Polynomial approximation on convex polytopes in \mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes. | ||
| 546 | |a Text in English. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Polytopes. | |
| 650 | 0 | |a Orthogonal polynomials. | |
| 650 | 0 | |a Geometry, Riemannian. | |
| 650 | 6 | |a Polytopes. | |
| 650 | 6 | |a Polynômes orthogonaux. | |
| 650 | 6 | |a Géométrie de Riemann. | |
| 650 | 7 | |a Geometry, Riemannian |2 fast | |
| 650 | 7 | |a Orthogonal polynomials |2 fast | |
| 650 | 7 | |a Polytopes |2 fast | |
| 710 | 2 | |a American Mathematical Society, |e publisher. | |
| 758 | |i has work: |a Polynomial approximation on polytopes (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGgcTDkbq4g64b9pdkdHhb |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Totik, V. |t Polynomial approximation on polytopes. |d Providence, Rhode Island : American Mathematical Society, 2014 |z 9781470416669 |w (DLC) 2014024664 |w (OCoLC)881721540 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1091. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5295324 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37444892 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL5295324 | ||
| 938 | |a YBP Library Services |b YANK |n 12358259 | ||
| 994 | |a 92 |b IZTAP | ||