Polynomial approximation on polytopes

✍ Scribed by Vilmos Totik

• Publisher: Amer Mathematical Society
• Year: 2014
• Tongue: English
• Leaves: 124
• Series: Memoirs of the American Mathematical Society 1091
• Category: Library

✦ Synopsis

Polynomial approximation on convex polytopes in d is considered in uniform and Lp-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the Lp -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