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- W4285077686 abstract "Let $Gamma subset mathbb C$ be a curve of class $C(2,alpha)$. For $z_{0}$ in the unbounded component of ${mathbb C}setminus Gamma$, and for $n=1,2,...$, let $nu_n$ be a probability measure with supp$(nu_{n})subset Gamma$ which minimizes the Bergman function $B_{n}(nu,z):=sum_{k=0}^{n}|q_{k}^{nu}(z)|^{2}$ at $z_{0}$ among all probability measures $nu$ on $Gamma$ (here, ${q_{0}^{nu},ldots,q_{n}^{nu}}$ are an orthonormal basis in $L^2(nu)$ for the holomorphic polynomials of degree at most $n$). We show that ${nu_{n}}_n$ tends weak-* to $hatdelta_{z_{0}}$, the balayage of the point mass at $z_0$ onto $Gamma$, by relating this to an optimization problem for probability measures on the unit circle. Our proof makes use of estimates for Faber polynomials associated to $Gamma$." @default.
- W4285077686 created "2022-07-13" @default.
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- W4285077686 date "2022-07-11" @default.
- W4285077686 modified "2023-10-18" @default.
- W4285077686 title "An extremal problem for the Bergman kernel of orthogonal polynomials" @default.
- W4285077686 doi "https://doi.org/10.48550/arxiv.2207.04662" @default.
- W4285077686 hasPublicationYear "2022" @default.
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