On difference operators for symmetric Krall-Hahn polynomials

On the Krall-type polynomials

Using a general and simple algebraic approach, some results on Krall-type orthogonal polynomials and some of their extensions are obtained. E-mail: [email protected], [email protected], [email protected]

Self-adjoint Difference Operators and Symmetric Al-salam–chihara Polynomials

The symmetric Al-Salam–Chihara polynomials for q > 1 are associated with an indeterminate moment problem. There is a self-adjoint second order difference operator on l(Z) to which these polynomials are eigenfunctions. We determine the spectral decomposition of this self-adjoint operator. This leads to a class of discrete orthogonality measures, which have been obtained previously by Christianse...

The q-Racah-Krall-type polynomials

WKB Approximation and Krall-Type Orthogonal Polynomials

Abstract. We give a unified approach to the Krall-type polynomials orthogonal with respect to a positive measure consisting of an absolutely continuous one ‘perturbed’ by the addition of one or more Dirac delta functions. Some examples studied by different authors are considered from a unique point of view. Also some properties of the Krall-type polynomials are studied. The threeterm recurrence...

Skew Divided Difference Operators and Schubert Polynomials

We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group. We also prove that, under certain assumptions, the skew divided difference operators transform the Schubert polynomials into polynomials with posit...