Orthogonal polynomials on generalized Julia sets
G\"okalp Alpan, Alexander Goncharov
TL;DR
This paper extends the theory of orthogonal polynomials to generalized Julia sets, analyzing equilibrium measures, Green function smoothness, and Parreau-Widom criteria for specific real cases.
Contribution
It introduces new results on orthogonal polynomials and equilibrium measures for generalized Julia sets, expanding prior work to broader classes.
Findings
Extended orthogonal polynomial results to generalized Julia sets
Analyzed smoothness of Green functions in this context
Established Parreau-Widom criterion for certain real Julia sets
Abstract
We extend results by Barnsley et al. about orthogonal polynomials on Julia sets to the case of generalized Julia sets. The equilibrium measure is considered. In addition, we discuss optimal smoothness of Green functions and Parreau-Widom criterion for a special family of real generalized Julia sets.
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