# Fast approximation on the real line

Presented by:
Arieh Iserles
Date:
Wednesday 7th August 2019 - 14:00 to 15:00
Venue:
INI Seminar Room 2
Abstract:
Abstract: While approximation theory in an interval is thoroughly understood, the real line represents something of a mystery. In this talk we review the state of the art in this area, commencing from the familiar Hermite functions and moving to recent results  characterising all orthonormal sets on $L_2(-\infty,\infty)$ that have a skew-symmetric (or skew-Hermitian) tridiagonal differentiation matrix and such that their first $n$ expansion coefficients can be calculated in $O(n \log n)$ operations. In particular, we describe the generalised Malmquist–Takenaka system. The talk concludes with a (too!) long list of open problems and challenges.

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.