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Polynomial approximation on polytopes

Author: V Totik
Publisher: Providence, Rhode Island : American Mathematical Society, 2014.
Series: Memoirs of the American Mathematical Society, no. 1091.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

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  Read more...

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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: V Totik
ISBN: 9781470416669 1470416662
OCLC Number: 881721540
Language Note: Text in English.
Notes: "Volume 232, number 1091 (third of 6 numbers), November 2014."
Description: v, 112 pages : illustrations ; 25 cm.
Contents: The result --
Outline of the proof --
Fast decreasing polynomials --
Approximation on simple polytopes --
Polynomial approximants on rhombi --
Pyramids and local moduli on them --
Local approximation on the sets K[alpha] --
Global approximation of F = Fn on S1/32 excluding a neighborhood of the apex --
Global approximation of f on S1/64 --
Completion of the proof of Theorem 1.1 --
Approximation in Rd --
A k-functional andthe equivalence theorem --
The Lp result --
Proof of the Lp result --
The dyadic decomposition --
Some properties of Lp moduli of smoothness --
Local Lp moduli of smoothness --
Local approximation --
Global Lp approximation excluding a neighborhood of the apex --
Strong direct and converse inequalities --
The K-functional in Lp and the equivalence theorem.
Series Title: Memoirs of the American Mathematical Society, no. 1091.
Responsibility: Vilmos Totik.

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