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.
- ISBN13 9781470416669
- Publish Date 30 October 2014
- Publish Status Active
- Publish Country US
- Imprint American Mathematical Society
- Format Paperback
- Pages 110
- Language English