Geronimus transformations for sequences of $d$-orthogonal polynomials

Abstract

In this paper an extension of the concept of Geronimus transformation for sequences of $d$-orthogonal polynomials $\{P_n\}$ is introduced. The transformed sequences $\{P^{(k)}_n\}$, for $ k=1,\ldots, d,$ are analyzed and some relationships between these new sequences of polynomials are given. Also the associated Hessenberg matrices and their transformed are studied.