Abstract
For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials {P n } to properties of the support. More precisely we relate the Julia set of P n to the outer boundary of the support, the filled Julia set to the polynomial convex hull K of the support, and the Green’s function associated with P n to the Green’s function for the complement of K.
Original language | English |
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Pages (from-to) | 401–413 |
Number of pages | 13 |
Journal | Potential Analysis |
Volume | 50 |
Issue number | 3 |
Early online date | 2018 |
DOIs | |
Publication status | Published - 2019 |
Subject classification (UKÄ)
- Mathematical Analysis
Free keywords
- Orthogonal polynomials
- Julia set
- Green’s function