Integral Equations and Operator Theory

, Volume 58, Issue 4, pp 449–475 | Cite as

The Algebra of Differential Operators Associated to a Weight Matrix

Article

Abstract.

Given a weight matrix W(x) of size N on the real line one constructs a sequence of matrix valued orthogonal polynomials, {Pn}n≥0. We study the algebra \({\mathcal{D}}(W)\) of differential operators D with matrix coefficients such that PnD = ΛnPn, with Λn in the algebra A of N × N complex matrices. We study certain representations of this algebra, prove that it is a *-algebra and give a precise description of its isomorphic image inside the algebra \({A^{{N}_0}}\).

Mathematics Subject Classification (2000).

Primary 33C45, 47L80 Secondary 47E05 

Keywords.

Matrix orthogonal polynomials bispectral problem algebra of differential operators ad-conditions adjoint operation 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.CIEM-FaMAFUniversidad Macional de CórdobaMacional de CórdobaArgentina

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