Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples
By M. Castro, F. Alberto Grünbaum. 2005
57 citations recorded by the source corpus.
Abstract We describe a few families of orthogonal matrix polynomials of size N × N satisfying first order differential equations. This problem differs from the recent efforts reported for instance in [7] (Orthogonal matrix polynomials satisfying second order differential equations, Internat. Math. Research Notices, 2004 : 10 (2004), 461–484) and [15] (Matrix valued orthogonal polynomials of the Jacobi type, Indag. Math. 14 nrs. 3, 4 (2003), 353–366). While we restrict ourselves to considering only first order operators, we do not make any assumption as to their symmetry. For simplicity we restrict to the case N = 2. We draw a few lessons from these examples; many of them serve to illustrate the fundamental difference between the scalar and the matrix valued case.
Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/69e24b942f3ac39bb312ba08ab738dcaadcd7d1e
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In Computational Theory and Mathematics
- David Damanik
- Alexander Pushnitski
- Barry Simon
- Maarten van Pruijssen
- Pablo Román
- Erik Koelink
- Doron S. Lubinsky
- Vilmos Totik
In Statistical and Nonlinear Physics
- Alexander Pushnitski
- David Damanik
- Maarten van Pruijssen
- Barry Simon
- Pablo Román
- Erik Koelink
- David Damanik
- Jasper V. Stokman
Citations in the corpus
- The Analytic Theory of Matrix Orthogonal Polynomials (2007, methodology): “The corresponding real line theory (MOPRL) is still more recent: Following early work of Krein [133] and Berezan’ski [9] on block Jacobi matrices, mainly as applied to self-adjoint extensions, there was a seminal paper of Aptekarev–Nikishin [4] and a flurry of papers since the 1990s [10, 11, 12, 14,”
- Matrix Valued Orthogonal Polynomials related to (SU(2) x SU(2),diag) (2010, background): “This, phenomenon which does not appear in the scalar, case has been recently studied in the literature (see for instance [5], [4]).”