TY - JOUR
T1 - Norm estimates for Chebyshev polynomials, I
AU - Schiefermayr, Klaus
AU - Zinchenko, Maxim
N1 - Publisher Copyright:
© 2021 The Authors
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/5
Y1 - 2021/5
N2 - In this paper, we extend the sharp upper bound of Christiansen et al. (2017) and the sharp lower bound of Schiefermayr (2008) to the case of weighted Chebyshev polynomials on subsets of [−1,1] for the weight w(x)=1−x2. We then analyse the norm of Chebyshev polynomials on a circular arc, prove monotonicity of the corresponding Widom factors, find exact values of their supremum and infimum, and obtain a new proof for their limit.
AB - In this paper, we extend the sharp upper bound of Christiansen et al. (2017) and the sharp lower bound of Schiefermayr (2008) to the case of weighted Chebyshev polynomials on subsets of [−1,1] for the weight w(x)=1−x2. We then analyse the norm of Chebyshev polynomials on a circular arc, prove monotonicity of the corresponding Widom factors, find exact values of their supremum and infimum, and obtain a new proof for their limit.
KW - Chebyshev polynomials on a circular arc
KW - Lower and upper bounds on Widom factors
KW - Weighted Chebyshev polynomials
UR - http://www.scopus.com/inward/record.url?scp=85101821088&partnerID=8YFLogxK
U2 - 10.1016/j.jat.2021.105561
DO - 10.1016/j.jat.2021.105561
M3 - Article
AN - SCOPUS:85101821088
SN - 0021-9045
VL - 265
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
M1 - 105561
ER -