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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]
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1091. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Chapter 1. The result Chapter 2. Outline of the proof Chapter 3. Fast decreasing polynomials Chapter 4. Approximation on simple polytopes Chapter 5. Polynomial approximants on rhombi Chapter 6. Pyramids and local moduli on them Chapter 7. Local approximation on the sets $K_a$ Chapter 8. Global approximation of $F=F_n$ on $S_{1/32}$ excluding a neighborhood of the apex Chapter 9. Global approximation of $f$ on $S_{1/64}$ Chapter 10. Completion of the proof of Theorem 1.1 Chapter 11. Approximation in ${\mathbf R}^d$ Chapter 12. A $K$-functional and the equivalence theorem Chapter 13. The $L^p$ result Chapter 14. Proof of the $L^p$ result Chapter 15. The dyadic decomposition Chapter 16. Some properties of $L^p$ moduli of smoothness Chapter 17. Local $L^p$ moduli of smoothness Chapter 18. Local approximation Chapter 19. Global $L^p$ approximation excluding a neighborhood of the apex Chapter 20. Strong direct and converse inequalities Chapter 21. The $K$-functional in $L^p$ and the equivalence theorem.