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SUMMARY:Orthogonal systems with a skew-symmetric differentiation matrix - 
 Marcus Webb (KU Leuven)
DTSTART:20180502T150000Z
DTEND:20180502T160000Z
UID:TALK105280@talks.cam.ac.uk
CONTACT:Andrew Celsus
DESCRIPTION:For certain time-dependent PDEs\, the norm of the solution as 
 time progresses necessarily decays\, or is preserved\, e.g. the diffusion\
 , Schrödinger\, or nonlinear advection equations\, a property due to the 
 skew-hermitian nature of the differentiation operator. For a numerical sol
 ution of these PDEs\, these properties of the underlying analytical soluti
 ons can be perfectly respected if the matrix representing differentiation 
 in your discretisation is skew-hermitian too. In this talk\, we characteri
 se all systems of orthogonal functions on L2(R) such that the differentiat
 ion matrix for an expansion in these functions is real\, skew-symmetric\, 
 tridiagonal and irreducible\, accomplished by interesting links between or
 thogonal polynomials\, the Fourier transform\, and Paley-Wiener band-limit
 ed function spaces. This is joint work with Arieh Iserles (Cambridge)\, wi
 th a preprint available at http://www.damtp.cam.ac.uk/user/na/NA_papers/NA
 2018_02.pdf.
LOCATION:MR14\, Centre for Mathematical Sciences
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