Asymptotics of Chebyshev polynomials. I: Subsets of \({\mathbb {R}}\)

DOI10.1007/s00222-016-0689-xzbMath1369.41031arXiv1505.02604OpenAlexW3121895607MaRDI QIDQ522197

Maxim Zinchenko, Barry Simon, Jacob Stordal Christiansen

Publication date: 13 April 2017

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.02604

zbMATH Keywords

potential theorypolar setharmonic measureFuchsian groupprobability measureMontel's theoremMöbius transformationHerglotz representationCoulomb energyFrostman's theoremalternation theoremBernstein-Walsh lemmaequilibrium potential, Green's functionfinite gap setisospectral torusJoukowski mapmonodromy theoremRobin constantspectrum of periodic Schrödinger operatorTotik-Widom theoremWirtinger calculus

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Polynomials and rational functions of one complex variable (30C10) Asymptotic representations in the complex plane (30E15)

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Norm estimates for Chebyshev polynomials. II ⋮ Twelve tales in mathematical physics: An expanded Heineman prize lecture ⋮ Norm estimates for Chebyshev polynomials, I. ⋮ The growth of polynomials outside of a compact set-the Bernstein-Walsh inequality revisited ⋮ Ahlfors problem for polynomials ⋮ Filled Julia sets of Chebyshev polynomials ⋮ Widom factors for generalized Jacobi measures ⋮ Periodic Jacobi matrices on trees ⋮ Some Asymptotics for Extremal Polynomials ⋮ Asymptotics of Chebyshev polynomials. V: Residual polynomials ⋮ Widom factors and Szegő-Widom asymptotics, a review ⋮ Asymptotics of Chebyshev Polynomials, III. Sets Saturating Szegő, Schiefermayr, and Totik–Widom Bounds ⋮ On the Widom factors for \(L_p\) extremal polynomials ⋮ Asymptotic Properties of Jacobi Matrices for a Family of Fractal Measures ⋮ Mini-workshop: Reflectionless operators: the Deift and Simon conjectures. Abstracts from the mini-workshop held October 22--28, 2017 ⋮ Asymptotics of Chebyshev polynomials. II: DCT subsets of \(\mathbb{R}\) ⋮ On Chebyshev polynomials in the complex plane ⋮ Orthogonal polynomials associated with equilibrium measures on \(\mathbb {R}\) ⋮ Asymptotics of Chebyshev polynomials. IV: Comments on the complex case ⋮ On the Totik-Widom property for a quasidisk ⋮ Sharp lower bounds for the Widom factors on the real line ⋮ Computation of Chebyshev polynomials for union of intervals ⋮ Szegő's condition on compact subsets of \(\mathbb{C}\) ⋮ Pointwise Remez inequality

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