Polynomial Approximation on Polytopes

Polynomial approximation on convex polytopes in is considered in uniform and -norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the -case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate -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.

• Author: Vilmos Totik
• Publisher: American Mathematical Soc.
• Published: 2014-09-29
• Pages: 124