BochnerPearson-type characterization of the free Meixner class Academic Article uri icon

abstract

  • The operator Lf(x)-f(y)x-yd(y) is, for a compactly supported measure with an L3 density, a closed, densely defined operator on L2(). We show that the operator Q=pL2-q L has polynomial eigenfunctions if and only if is a free Meixner distribution. The only time Q has orthogonal polynomial eigenfunctions is if is a semicircular distribution. More generally, the only time the operator p(LL)-qL has orthogonal polynomial eigenfunctions is when measures and are related by a Jacobi shift. 2010 Elsevier Inc. All rights reserved.

published proceedings

  • Advances in Applied Mathematics

author list (cited authors)

  • Anshelevich, M.

citation count

  • 6

complete list of authors

  • Anshelevich, Michael

publication date

  • January 2011