Widom factors

Date
2015
Authors
Goncharov, A.
Hatinoğlu, B.
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Logarithmic capacity
Print ISSN
0926-2601
Electronic ISSN
1572-929X
Publisher
Springer Netherlands
Volume
42
Issue
3
Pages
671 - 680
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Series
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.

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Book Title
Keywords
Chebyshev numbers, Cantor sets
Citation
Published Version (Please cite this version)