Mason, J.C. (2005) The minimality properties of Chebyshev polynomials and their lacunary series. Numerical Algorithms, 38 (1). pp. 61-78. ISSN 1017-1398

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