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A remark on concentration of the error between a function and its best polynomial approximants

Published online by Cambridge University Press:  12 July 2007

S. P. Zhou
S. P. Zhou
Affiliation:
Institute of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China and Faculty of Science, Hangzhou Institute of Electronics Engineering, Hangzhou, Zhejiang 310037, People's Republic of China
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Abstract

By a new approach and different techniques, the present paper will give an essential generalization of a main theorem of Hasson. We also show that there do exist functions that satisfy the condition in our theorem, which we suggest to replace Hasson's condition (H1) or (H2) (for k = 1), but do not satisfy Hasson's condition. This gives a negative answer to a question raised by Hasson.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 2 , April 2003 , pp. 467 - 476
Copyright
Copyright © Royal Society of Edinburgh 2003

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