02530cam  22003978i 450000100090000000300050000900500170001400600190003100700150005000800410006502000270010604000240013305000210015708200170017810000140019524500830020926300090029226400700030130000340037133600210040533700250042633800230045149000740047450400410054850510360058950600500162553300950167553800360177058800470180665000150185365000280186865000260189677601180192285600440204085600480208418197187RPAM20170613145040.0m      b    000 0 cr/|||||||||||170613s2014    riu     ob    000 0 eng    a9781470418946 (online)  aDLCbengerdadRPAM00aQA691b.T68 201400a516/.1582231 aTotik, V.10aPolynomial approximation on polytopes /h[electronic resource] cVilmos Totik.  a1411 1aProvidence, Rhode Island :bAmerican Mathematical Society,c2014.  a1 online resource (pages cm.)  atext2rdacontent  aunmediated2rdamedia  avolume2rdacarrier0 aMemoirs of the American Mathematical Society, x1947-6221 ; vv. 1091  aIncludes bibliographical references.00tChapter 1. The resulttChapter 2. Outline of the prooftChapter 3. Fast decreasing polynomialstChapter 4. Approximation on simple polytopestChapter 5. Polynomial approximants on rhombitChapter 6. Pyramids and local moduli on themtChapter 7. Local approximation on the sets $K_a$tChapter 8. Global approximation of $F=F_n$ on $S_{1/32}$ excluding a neighborhood of the apextChapter 9. Global approximation of $f$ on $S_{1/64}$tChapter 10. Completion of the proof of Theorem 1.1tChapter 11. Approximation in ${\mathbf R}^d$tChapter 12. A $K$-functional and the equivalence theoremtChapter 13. The $L^p$ resulttChapter 14. Proof of the $L^p$ resulttChapter 15. The dyadic decompositiontChapter 16. Some properties of $L^p$ moduli of smoothnesstChapter 17. Local $L^p$ moduli of smoothnesstChapter 18. Local approximationtChapter 19. Global $L^p$ approximation excluding a neighborhood of the apextChapter 20. Strong direct and converse inequalitiestChapter 21. The $K$-functional in $L^p$ and the equivalence theorem1 aAccess is restricted to licensed institutions  aElectronic reproduction.bProvidence, Rhode Island :cAmerican Mathematical Society.d2014  aMode of access : World Wide Web  aDescription based on print version record. 0aPolytopes. 0aOrthogonal polynomials. 0aGeometry, Riemannian.0 iPrint version: aTotik, V.tPolynomial approximation on polytopes /w(DLC)   2014024664x0065-9266z97814704166694 3Contentsuhttp://www.ams.org/memo/1091/4 3Contentsuhttps://doi.org/10.1090/memo/1091