## Abstract

We consider matrix polynomials orthogonal with respect to a sesquilinear form ⟨ · , · ⟩ _{W}, such that ⟨P(t)W(t),Q(t)W(t)W⟩=∫_{I}P(t)dμQ(t)^{T},P,Q∈P^{p×p[t]},where μ is a symmetric, positive definite matrix of measures supported in some infinite subset I of the real line, and W(t) is a matrix polynomial of degree N. We deduce the integral representation of such sesquilinear forms in such a way that a Sobolev-type inner product appears. We obtain a connection formula between the sequences of matrix polynomials orthogonal with respect to μ and ⟨ · , · ⟩ _{W}, as well as a relation between the corresponding block Jacobi and Hessenberg type matrices.

Original language | English |
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Pages (from-to) | 5009-5032 |

Number of pages | 24 |

Journal | Mediterranean Journal of Mathematics |

Volume | 13 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1 Dec 2016 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2016, Springer International Publishing.

## All Science Journal Classification (ASJC) codes

- General Mathematics