Institute of Mathematics for Industry

Seminar



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Construction of the exceptional orthogonal polynomials and its application to the superintegrable system


Hold Date 2013-05-21 10:30~2013-05-21 12:00

Place Seminar Room 4, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Satoshi Tsujimoto (Kyoto University)

Abstract:
To construct systems of polynomial eigenfunctions with jump in degree by means of the theory of Darboux transformation, a class of eigenfunctions of the Sturm-Liouville operator is introduced. Then we show a systematic way to construct the system of polynomial eigenfunctions with jump in degree from the Sturm-Liouville operator of the classical orthogonal polynomial. We classify these systems of the polynomial eigenfunctions with jump in degree according to the contour of integration. Finally, we give a brief review on the superintegrable Hamiltonian derived from the exceptional orthogonal polynomials.