Widom factors

Date

2015

Authors

Goncharov, A.
Hatinoğlu, B.

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Abstract

Given a non-polar compact set K,we define the n-th Widom factor Wn(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 Mn. We also present a set K with highly irregular behavior of the Widom factors.

Source Title

Logarithmic capacity

Publisher

Springer Netherlands

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Published Version (Please cite this version)

Language

English