Bochner-Pearson-type characterization of the free Meixner class Academic Article

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.

authors

• Anshelevich, Michael

published proceedings

• ADVANCES IN APPLIED MATHEMATICS

author list (cited authors)

• Anshelevich, M.

citation count

• 9

complete list of authors

• Anshelevich, Michael

publication date

• January 2011

publisher

• Elsevier  Publisher

published in

• Advances in Applied Mathematics  Journal

keywords

• Bochner's Theorem
• Free Meixner Distributions

Digital Object Identifier (DOI)

• 10.1016/j.aam.2010.01.011

start page

• 25

end page

• 45

volume

• 46

issue

• 1-4

URL

• http://dx.doi.org/10.1016/j.aam.2010.01.011