11 Mar 2008; * Mat-Nat
Faculty (UiTø), room A228.
Thursday 10:15-12:00
(notice time/date)*

Boris Shapiro (Stockholm University, Sweden)

"On root asymptotics for polynomial and entire eigenfunctions".

A univariate differential operator T=\sum_{i=1}^k Q_k(x) d/ dx^k with polynomial coefficients is called exactly solvable if deg Q_i is at most i and there exists at least one value of index for which one has the equality. A simple linear algebra shows that any exactly solvable T has exactly one polynomial eigenfunction in each sufficiently large degree.

In this talk we will give a detailed description of the root asymptotics of these eigenfunctions. We will also describe results of similar flavor for the classical case of the Schrödinger operator with polynomial potential.