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Fast approximation on the real line

Presented by: 
Arieh Iserles
Wednesday 7th August 2019 - 14:00 to 15:00
INI Seminar Room 2
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons