Chebyshev constants and the inheritance problem |
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| Authors: | Vilmos Totik |
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| Institution: | aBolyai Institute, Analysis Research Group of the Hungarian Academy of Sciences, University of Szeged, Szeged, Aradi v. tere 1, 6720, Hungary;bDepartment of Mathematics, University of South Florida, 4202 E. Fowler Ave, PHY 114, Tampa, FL 33620-5700, USA |
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| Abstract: | It is proven that any set E consisting of finitely many intervals can be approximated with order 1/n by polynomial inverse images of -1,1]. This leads to a new proof of the fact that the n-th Chebyshev constant is  Kcap(E)n with some K independent of n. The proof uses properties of monotone systems, in particular, the statement in the so-called inheritance problem. |
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| Keywords: | Chebyshev constants Sets of finitely many intervals Logarithmic capacity Inheritance problem |
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