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      Widom factors

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      Author
      Goncharov, A.
      Hatinoğlu, B.
      Date
      2015
      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
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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.
      Keywords
      Chebyshev numbers
      Cantor sets
      Permalink
      http://hdl.handle.net/11693/22170
      Published Version (Please cite this version)
      https://doi.org/10.1007/s11118-014-9452-3
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      • Department of Mathematics 644
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