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SUMMARY:Approximation on the Real Line - Prof. Arieh Iserles (DAMTP)
DTSTART:20181112T203000Z
DTEND:20181112T213000Z
UID:TALK114226@talks.cam.ac.uk
CONTACT:73969
DESCRIPTION:The purpose of the exercise is simple\, to design an orthogona
 l basis in the space of square-integrable functions on the real line such 
 that the linear map taking the basis to its derivatives is skew symmetric.
  Such bases possess numerous advantages in the computation of ODEs and PDE
 s. In this talk\, based on a joint work with Marcus Webb\, I will complete
 ly characterise all such orthogonal systems using Fourier analysis and the
  theory of orthogonal polynomials. The extension of this work to complex-v
 alued skew-Hermitian `differentiation matrices’ is trivial but it leads 
 to a beautiful outcome\, an orthogonal system of rational functions design
 ed (in a different context) almost a century ago by Malmquist and Takenaka
  and which exhibits some truly miraculous properties.
LOCATION:Winstanley Lecture Theatre\, Trinity College
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