Asymptotics of Chebyshev polynomials, I : subsets of R
We consider Chebyshev polynomials, (Formula presented.), for infinite, compact sets (Formula presented.) (that is, the monic polynomials minimizing the (Formula presented.)-norm, (Formula presented.), on (Formula presented.)). We resolve a (Formula presented.) year old conjecture of Widom that for finite gap subsets of (Formula presented.), his conjectured asymptotics (which we call Szegő–Widom as
