Presented by:
Arieh Iserles
Date:
Wednesday 7th August 2019 - 14:00 to 15:00
Venue:
INI Seminar Room 2
Event:
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.
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