## Department Colloquium

### Friday, September 21st, 2018

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Boris Levit (Queen's University)

**Title:** Optimal Cardinal Interpolation in Approximation Theory, Nonparametric Regression, and Optimal Design

**Abstract: ** For the Hardy classes of functions analytic in the strip around real axis of a size $2\beta$, an optimal method of cardinal interpolation has been proposed within the framework of Optimal Recovery. It will be shown that this method, based on the Jacobi elliptic functions, is also optimal according to the criteria of Nonparametric Regression and Optimal Design. In a stochastic non-asymptotic setting, the maximal mean squared error of the optimal interpolant is evaluated explicitly, for all noise levels away from $0$. A pivotal role is played by the interference effect, in which the oscillations exhibited by the interpolant's bias and variance mutually cancel each other. In the limiting case $\beta \rightarrow \infty $, the optimal interpolant converges to the well known Nyquist-Shannon cardinal sampling series.