Abstract
In this contribution, we explore the well-known connection between Hurwitz and orthogonal polynomials. Namely, given a Hurwitz polynomial, it is shown that it can be decomposed into two parts: a polynomial that is orthogonal with respect to some positive measure supported in the positive real axis and its corresponding second-kind polynomial. Conversely, given a sequence of orthogonal polynomials with respect to a positive measure supported in the positive real axis, a sequence of Hurwitz polynomials can be constructed. Based on that connection, we construct sequences of Hurwitz polynomials that satisfy a recurrence relation, in a similar way as the orthogonal polynomials do. Even more, we present a way to construct families of Hurwitz polynomials using two sequences of parameters and a recurrence relation that constitutes an analogue of Favard's theorem in the theory of orthogonal polynomials.
Original language | English |
---|---|
Pages (from-to) | 2191-2208 |
Number of pages | 18 |
Journal | Linear and Multilinear Algebra |
Volume | 67 |
Issue number | 11 |
DOIs | |
Publication status | Published - 2 Nov 2019 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory