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Polynomial Approximation on Polytopes
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Artikel-Nr:
9781470418946
Einband:
PDF
Seiten:
112
Autor:
Vilmos Totik
eBook Typ:
PDF
eBook Format:
PDF
Kopierschutz:
Adobe DRM [Hard-DRM]
Sprache:
Deutsch
Beschreibung:
Polynomial approximation on convex polytopes in $mathbf{R}^d$ is considered in uniform and $L^p$-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the $L^p$-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.
Polynomial approximation on convex polytopes in $mathbf{R}^d$ is considered in uniform and $L^p$-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the $L^p$-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.