Abstract
Given a non-polar compact set K,we define the n-th Widom factor W n (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 \((W_{n}(K))_{n=1}^{\infty }\) has subexponential growth. Our aim is to consider compact sets with maximal growth of the Widom factors. We show that for each sequence \((M_{n})_{n=1}^{\infty }\) of subexponential growth there is a Cantor-type set whose Widom’s factors exceed M n . We also present a set K with highly irregular behavior of the Widom factors.
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Goncharov, A., Hatinoğlu, B. Widom Factors. Potential Anal 42, 671–680 (2015). https://doi.org/10.1007/s11118-014-9452-3
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DOI: https://doi.org/10.1007/s11118-014-9452-3