Abstract
Considered are the monic polynomials orthogonal with respect to the equilibrium measure on the family of Julia sets for the complex mappings z → (z-λ)2 where λ is a parameter. When λ = 2 they are the Chebychev polynomials on [0,4]. For all λ ε C an infinite subsequence of the polynomials can be calculated; for λ > 0 they have the equal oscillation property on the Julia set, and for λ ε (0,2] their zeros “interlace” on an underlying tree structure. They are relevant to approximation theory for functions defined on the Julia set.
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© 1982 Birkhäuser Verlag Basel
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Barnsley, M.F., Geronimo, J.S., Harrington, A.N., Dager, L.D. (1982). Approximation Theory on a Snowflake. In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory II. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 61. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7189-1_2
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DOI: https://doi.org/10.1007/978-3-0348-7189-1_2
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