On semiclassical linear functionals of class s=2: classification and integral representations

Abstract

In this paper, we obtain all the semiclassical linear functionals of class two taking into account the irreducible expression of the corresponding Pearson equation. We focus our attention in their integral representations. Thus, some linear functionals very well known in the literature, associated with perturbations of classical linear functionals, as well as new linear functionals appear which have not been studied as far as we know.

Keywords:

• orthogonal polynomials
• semiclassical linear functionals
• integral representations

2000 Mathematics Subject Classification::

• 42C05
• 33C45

Acknowledgements

The work of F. Marcellán has been supported by Dirección General de Investigación, Ministerio de Ciencia e Innovación of Spain, grant MTM2009-12740-C03-01. The authors thank the referees for their suggestions and remarks in order to improve the presentation of the manuscript.

Notes

1. [email protected]

2. [email protected]

Additional information

Notes on contributors

M. Sghaier

1

M. Zaatra

2