# PDE and Analysis Seminar: Grzegorz Swiderski (Wroclaw)

Title: Asymptotics of Christoffel functions in an unbounded setting Abstract: Consider a measure $\mu$ supported on the real line with all moments finite. Let $(p_n : n \geq 0)$ be the corresponding sequence of orthonormal polynomials. This sequence satisfies the three-term recurrence relation $a_{n-1} p_{n-1}(x) + b_n p_n(x) a_n p_{n+1}(x) = x p_n(x) \quad (n > 0)$ for some sequences $a$ and $b$. One defines the $n$th Christoffel function by $\lambda_n(x) = \left[ \sum_{k=0}^n p_k(x)^2 \right]^{-1}.$ In the talk, under some regularity hypotheses on $a$ and $b$, we show exact asymptotics of the sequence $(\lambda_n(x) : n \geq 0)$ in the case when $\textrm{supp}(\mu) = \mathbb{R}$.

## Date:

Thu, 27/04/2017 - 13:00 to 14:00

Ross 70