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On polynomial eigenfunctions for linear ordinary differential operators with polynomial coefficients and related problems
  KTH/Nordita/SU seminar in Theoretical Physics [before December 2013]

Wednesday 24 March 2010
from 11:00 to 12:00
at FA31
Speaker : B.Shapiro (Matematiska Inst, SU)
Abstract : I present some new results on the asymptotic root distribution of generalized polynomial eigenfunctions for a large class of univariate linear differential operators. For example, an operator T=Q_k(x)D^k+...+ Q_1(x)D, where D=d/dx and Q_i(x) are polynomials is called exactly solvable if for almost any polynomial p (x) the degree of T(p(x)) equals the degree of p(x). One can easily show that for any such T there exists and unique ( up to a scalar factor) eigenpolynomial p_n(x) of degree n for all sufficiently large n. I will describe, in particular, the asymptotical root distribution of p_n(x) when n->oo illustrated on the attached picture.
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