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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.
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 o...
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關於作者
Vilmos Totik, Bolyai Institute, University of Szeged, Hungary.
Vilmos Totik, Bolyai Institute, University of Szeged, Hungary.
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