arXiv subjects

Abdessadek Saib

Publications and source records attributed to Abdessadek Saib.

2 recordsLinked to original sources

arXiv2021

Some new perspectives on d-orthogonal polynomials

The aim of this paper is twofold. The first part is concerned with the associated and the so-called co-polynomials, i.e. new sequences obtained when finite perturbations of the recurrence coefficients are considered. In the second part we present nice Casorati determinants with co-polynomials entries. We look at Darboux factorization of lower Hessenberg matrices and the corresponding polynomials, then combine it with totally nonnegative matrices to find out sufficient conditions for zeros to be real and distinct. In addition, kernel polynomials, d-symmetric sequences as well as quasi-orthogonality from linear combination are discussed as well. Therefore, new characterization of the d-quasi-orthogonality which corresponds to the first structure relation in the standard case is constructed.

math.CA↗

arXiv2020

On Mittag-Leffler d-orthogonal polynomials

This paper presents a first result of a long term research project dealing with the construction of d-orthogonal polynomials with Hahn's property. We shall show that the latter class could be characterized by expanding a polynomial as a finite sum of first derivatives of the elements of the sequence and we shall explain how this characterization could be used to construct Hahn-classical d-orthogonal polynomials as well. In this paper we look for solutions of linear combinations of the first derivatives of two consecutive elements of the sequence by considering the derivative operator and Delta (discrete) operator. The resulting polynomials constitute a particular class of Laguerre d-orthogonal polynomials and a generalization of Mittag-Leffler polynomials, respectively.

math.CA↗