2014/01/24 by Vilmos Totik, Totik, Vilmos, Peter Yuditskii +1
Mathematics · #31A15 #42C05 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #math.CA #math.CV #msc:31A15 #msc:42C05
paper · pdf · doi:10.48550/arxiv.1401.6357
Dedicated to the memory of two outstanding mathematicians, Andrei Aleksandrovich Gonchar and Herbert Stahl
arxiv created 2014/01/24 · arxiv updated 2014/01/27
In 1969 Harold Widom published his seminal paper, which gave a complete description of orthogonal and Chebyshev polynomials on a system of smooth Jordan curves. When there were Jordan arcs present the theory of orthogonal polynomials turned out to be just the same, but for Chebyshev polynomials Widom's approach proved only an upper estimate, which he conjectured to be the correct asymptotic behavior. In this note we make some clarifications which will show that the situation is more complicated.