The Darboux process and time-and-band limiting for matrix orthogonal polynomials. (English) Zbl 1326.33013
Summary: We extend to a situation involving matrix valued orthogonal polynomials a scalar result that originates in work of Claude Shannon in laying the mathematical foundations of information theory and a remarkable series of papers by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960’s. We show that in this case an algebraic miracle that plays a very important role in the classical case survives an application of the so-called Darboux process in the matrix valued context.
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 22E45 | Representations of Lie and linear algebraic groups over real fields: analytic methods |
| 33C47 | Other special orthogonal polynomials and functions |
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