E. A. Rakhmanov

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math.CA2025

Flow of the zeros of polynomials under iterated differentiation

Andrei Martinez-Finkelshtein, Evgenii A. Rakhmanov

For a monic polynomial $Q_{n}$ of degree $n$ , let $Q_{n, k}$ be its $k$ -th derivative normalized to be monic. Under the only assumption that the sequence ${Q_{n}}$ has a weak* limiti…

math.CA2025

Weighted equilibrium and the flow of derivatives of polynomials

Andrei Martinez-Finkelshtein, Evgenii A. Rakhmanov

Given a sequence of polynomials $Q_{n}$ of degree $n$ with zeros on $[- 1, 1]$ , we consider the triangular table of derivatives $Q_{n, k} (x) = d^{k} Q_{n} (x) / d x^{k}$ . Under the assumption th…