Widom factors
Author
Goncharov, A.
Hatinoğlu, B.
Date
2015Source Title
Logarithmic capacity
Print ISSN
0926-2601
Electronic ISSN
1572-929X
Publisher
Springer Netherlands
Volume
42
Issue
3
Pages
671 - 680
Language
English
Type
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Abstract
Given a non-polar compact set K,we define the n-th Widom factor W<inf>n</inf>(K) as the ratio of the sup-norm of the n-th Chebyshev polynomial on K to the n-th degree of its logarithmic capacity. By G. Szegő, the sequence (Formula presented.) has subexponential growth. Our aim is to consider compact sets with maximal growth of the Widom factors. We show that for each sequence (Formula presented.) of subexponential growth there is a Cantor-type set whose Widom’s factors exceed M<inf>n</inf>. We also present a set K with highly irregular behavior of the Widom factors.