http://worldcat.org/entity/work/id/1917776554

Polynomial approximation on polytopes

Polynomial approximation on convex polytopes in Rd 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 1980's when some of the present findings were established for special, so called simple polytopes.

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