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Spectral decomposition and matrix-valued orthogonal polynomials |
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| Authors: | Wolter Groenevelt Mourad EH Ismail Erik Koelink |
| Institution: | 1. Technische Universiteit Delft, DIAM, EWI, Postbus 5031, 2600 GA Delft, The Netherlands;2. Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA;3. King Saud University, Riyadh, Saudi Arabia;4. Radboud Universiteit Nijmegen, IMAPP, FNWI, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands |
| Abstract: | The relation between the spectral decomposition of a self-adjoint operator which is realizable as a higher order recurrence operator and matrix-valued orthogonal polynomials is investigated. A general construction of such operators from scalar-valued orthogonal polynomials is presented. Two examples of matrix-valued orthogonal polynomials with explicit orthogonality relations and three-term recurrence relation are presented, which both can be considered as 2×2-matrix-valued analogues of subfamilies of Askey–Wilson polynomials. |
| Keywords: | Matrix-valued orthogonal polynomials Spectral theory |
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