The Minimality Properties of Chebyshev Polynomials and Their Lacunary Series |
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| Authors: | JC Mason |
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| Institution: | (1) School of Computing and Engineering, University of Huddersfield, Queensgate, Huddersfield, HD1 3DH, UK |
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| Abstract: | By considering four kinds of Chebyshev polynomials, an extended set of (real) results are given for Chebyshev polynomial minimality in suitably weighted Hölder norms on –1,1], as well as (L
 ) minimax properties, and best L
1 sufficiency requirements based on Chebyshev interpolation. Finally we establish best L
p
, L
and L
1 approximation by partial sums of lacunary Chebyshev series of the form 
i=0
a
i
 b
i(x) where
n
(x) is a Chebyshev polynomial and b is an odd integer  3. A complete set of proofs is provided. |
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| Keywords: | theory of best and near-best polynomial approximation L
p
L
1 and L
2 norms on [– 1 1] projections by Chebyshev series and Chebyshev interpolation Chebyshev polynomials of 1st 2nd 3rd and 4th kinds lacunary Chebyshev series |
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