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Session III.7 - Special Functions and Orthogonal Polynomials - Semi-plenary talk

Tuesday, June 20, 15:00 ~ 16:00

Exceptional orthogonal polynomials and isospectral deformations

Robert Milson

Dalhousie University, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak5e68ba14c1eb9bf1850ac62e8a227c1f').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy5e68ba14c1eb9bf1850ac62e8a227c1f = 'rm&#105;ls&#111;n' + '&#64;'; addy5e68ba14c1eb9bf1850ac62e8a227c1f = addy5e68ba14c1eb9bf1850ac62e8a227c1f + 'd&#97;l' + '&#46;' + 'c&#97;'; var addy_text5e68ba14c1eb9bf1850ac62e8a227c1f = 'rm&#105;ls&#111;n' + '&#64;' + 'd&#97;l' + '&#46;' + 'c&#97;';document.getElementById('cloak5e68ba14c1eb9bf1850ac62e8a227c1f').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy5e68ba14c1eb9bf1850ac62e8a227c1f + '\'>'+addy_text5e68ba14c1eb9bf1850ac62e8a227c1f+'<\/a>';

Exceptional ortogonal polynomials are solutions of second-order Sturm-Liouville problems. However, unlike their classical counter-parts the families in questions consist of polynomials that are missing a finite number of degrees. I will report on some recent work that allows for the construction of excpetional Jacobi polynomials with an aribtrary number of continuous parameters. These parameters serve as deformation parameters for isospectrally equivalent families of self-adjoint operators. Time permitting, we will describe the role of these new construction in the ongoing classification project for exceptional orthogonal polynomials.

Joint work with David Gomez-Ullate, MariaAngeles Garcia Ferrero.