Chebyshev constants for the unit circle. (16th October 2012)

• Record Type: Journal Article
• Authors: Ambrus, Gergely; Ball, Keith M.; Erdélyi, Tamás
• Is Part Of: Bulletin of the London Mathematical Society. Volume 45:Part 2(2013:Apr.)
• Page Start: 236
• Page End: 248
• Publication Date: 2012-10-16
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms/bds082
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract : It is proven that for any system of n points z 1, …, z n on the (complex) unit circle, there exists another point z of norm 1, such that∑ 1 | z k − z | 2 ⩽ n 2 4 . Two proofs are presented: one uses a characterization of equioscillating rational functions, while the other is based on Bernstein's inequality.