Recursive Procedures for Krall-Sheffer Operators
Mathematical Physics
2013-07-02 v3 math.MP
Exactly Solvable and Integrable Systems
Abstract
We consider the Krall-Sheffer class of admissible, partial differential operators in the plane. We concentrate on algebraic structures, such as the role of commuting operators and symmetries. For the polynomial eigenfunctions, we give explicit forms of the the level recurrence relations and differential raising operators, which are shown to satisfy unusual commutation relations. We present new generating functions for two of the cases.
Cite
@article{arxiv.1211.3075,
title = {Recursive Procedures for Krall-Sheffer Operators},
author = {Allan P. Fordy and Michael J. Scott},
journal= {arXiv preprint arXiv:1211.3075},
year = {2013}
}
Comments
26 pages, 7 figures, Several errors corrected. This is the final version as returned for publication in the journal