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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Orthogonal structure in and on quadratic surfaces
- Yuan Xu (University of Oregon)
DTSTART;TZID=Europe/London:20190620T133000
DTEND;TZID=Europe/London:20190620T142000
UID:TALK126283AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/126283
DESCRIPTION:Orthogonal structure in and on quadratic surfaces
Text of abstract: Spherical harmonics are orthogon
al polynomials on the unit sphere. They are eigenf
unctions of the Laplace-Beltrami operator on the s
phere and they satisfy an addition formula (a clos
ed formula for their reproducing kernel). In this
talk\, we consider orthogonal polynomials on quadr
atic surfaces of revolution and inside the domain
bounded by quadratic surfaces. \; We will defi
ne orthogonal polynomials on the surface of a cone
that possess both characteristics of spherical ha
rmonics. In particular\, the addition formula on t
he cone has a one-dimensional structure\, which le
ads to a convolution structure on the cone useful
for studying Fourier orthogonal series. Furthermor
e\, the same narrative holds for orthogonal polyno
mials defined on the solid cones.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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