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SUMMARY:Exceptional orthogonal polynomials - David Gomez-Ullate (ICMAT and
  Universidad Complutense de Madrid)
DTSTART:20170531T130000Z
DTEND:20170531T140000Z
UID:TALK72306@talks.cam.ac.uk
CONTACT:Rachel Furner
DESCRIPTION:Exceptional orthgonal polynomials are families of complete ort
 hogonal polynomials that arise as eigenfunctions of a Sturm-Liouville prob
 lem\, which differ from the classical families of Hermite\, Laguerre and J
 acobi in that there is a finite number of gaps in their degree sequence. D
 espite the "missing" degrees\, the remaining polynomials still span a comp
 lete basis of a weighted L2 space\, and the orthogonality weight is a rati
 onal modification of a classical weight.\nWe will briefly review the main 
 results in the theory of exceptional orthogonal polynomials (classificatio
 n\, position of their zeros\, recurrence relations\, etc.)\, with emphasis
  on the similarities and differences with classical polynomials.\nWe will 
 discuss some applications in mathematical physics and Painlevé equations 
 and end up with some questions on their potential use for numerical analys
 is and approximation theory.\n\n[1] D. Gomez-Ullate\, N. Kamran\, R. Milso
 n\, An extended class of orthogonal polynomials defined by a Sturm–Liouv
 ille problem\, J. Math. Anal. Appl. 359 (1)\, 352-367 (2009).\n[2] D. Gome
 z-Ullate\, A. Kasman\, A. Kuijlaars\, R. Milson\, Recurrence relations for
  exceptional Hermite polynomials\, J. Approx. Theory 204\, 1-16 (2016)\n[3
 ]  M. A. Garcia-Ferrero\, D. Gomez-Ullate\, Oscillation theorems for the W
 ronskian of an arbitrary sequence of eigenfunctions of Schrödinger’s eq
 uation\, Lett. Math. Phys. 105 (4)\, 551-573 (2015)\n[4] D. Gomez-Ullate\,
  Y. Grandati\, R. Milson\, Rational extensions of the quantum harmonic osc
 illator and exceptional Hermite polynomials\, J. Phys. A 47 (1)\, 015203 (
 2014).\n[5] D. Gomez-Ullate\, N. Kamran\, R. Milson\, A conjecture on exce
 ptional orthogonal polynomials\, Found. Comput. Math. 13 (4)\, 615-666 (20
 13)\n\n\n
LOCATION:MR11 CMS
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