Orthogonal- and Chebyshev polynomials on two intervals

DOI10.1007/BF01950935zbMath0726.33006MaRDI QIDQ802815

Franz Peherstorfer

Publication date: 1990

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

zbMATH Keywords

Chebyshev polynomialsrecurrence relation

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Approximations and expansions (41A99)

Related Items (14)

Inverse polynomial mappings and interpolation on several intervals ⋮ Minimal polynomials for compact sets of the complex plane ⋮ On Bernstein-Szegö orthogonal polynomials on several intervals. II: Orthogonal polynomials with periodic recurrence coefficients ⋮ Unnamed Item ⋮ The order of Lebesgue constant of Lagrange interpolation on several intervals ⋮ Bernstein-Type Polynomials on Several Intervals ⋮ A new approach to the generalized trace formula and asymptotics of Turán's determinant for polynomials with asymptotically \(N\)-periodic recurrence coefficients ⋮ Inverse polynomial images which consists of two Jordan arcs-an algebraic solution ⋮ Chebyshev polynomials for disjoint compact sets ⋮ Deformation of minimal polynomials and approximation of several intervals by an inverse polynomial mapping ⋮ Deformations of the Zolotarev polynomials and Painlevé VI equations ⋮ Trace formula for orthogonal polynomials with asymptotically 2-periodic recurrence coefficients ⋮ On Chebyshev-Markov rational functions over several intervals ⋮ Orthogonal and extremal polynomials on several intervals

Cites Work

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• Zolotarev's first problem - the best approximation by polynomials of degree \(\leq n-2\) to \(x^ n-n\sigma x^{n-1}\) in [-1,1]
• Orthogonal polynomials with asymptotically periodic recurrent coefficients
• Orthogonal polynomials in \(L^ 1\)-approximation
• Interlacing properties of the zeros of the error functions in best \(L^p\)- approximations
• Orthogonal polynomials and Padé approximants associated with a system of arcs
• On Cubic Transformations of Orthogonal Polynomials
• Simplified Treatment of Integrals of Cauchy Type, the Hilbert Problem and Singular Integral Equations. Appendix: Poincaré-Bertrand Formula

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