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Yu-Tian Li

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Preprint Aug 2026

The Erd\'elyi--Magnus--Nevai and Krasikov Conjectures for Jacobi Polynomials

Let $p_n^{(\alpha,\beta)}$ denote the Jacobi polynomial orthonormal for the weight $(1-x)^\alpha(1+x)^\beta$ on $[-1,1]$, where $\alpha,\beta\ge-1/2$, and put $S=\alpha+\beta+1$. We prove the uniform degree--parameter estimate $$ (1-x)^{\alpha+1/2}(1+x)^{\beta+1/2} \bigl|p_n^{(\alpha,\beta)}(x)\bigr|^2 \le C\max\bigl\{...

Qi-Feng Bai, Yu-Tian Li · 1 citation · ⚡1

Preprint Aug 2026

The Koornwinder--Kostenko--Teschl Conjecture for Jacobi Polynomials and the Discrete Laguerre Phase Transition

We prove the refined Koornwinder--Kostenko--Teschl conjecture. For the normalized weighted Jacobi function and all $n\in\mathbb N\_0$, $\alpha,\beta\ge0$, and $-1\le x\le1$, $$ |g\_n^{(\alpha,\beta)}(x)| \le \left[ \frac{(n+1)(n+\alpha+\beta+1)} {(n+\alpha+1)(n+\beta+1)} \right]^{1/4}\le1. $$ The proof combines a centr...

Yu-Tian Li · 0 citations