✦ LIBER ✦
Matrix polynomials satisfying first order differential equations and three term recurrence relations
✍ Scribed by Mirta M. Castro
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 546 KB
- Volume
- 233
- Category
- Article
- ISSN
- 0377-0427
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✦ Synopsis
We describe families of matrix valued polynomials satisfying simultaneously a first order differential equation and a three term recurrence relation. Our goal is to address the classification of the matrix valued polynomials satisfying first order differential equations through the solutions of the so-called bispectral problem. At the heart of this lies the need to solve some complicated nonlinear equations with matrix coefficients called ad-conditions. The solutions of these equations are studied under a variety of sufficient conditions on its coefficients.