Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials
نویسنده
چکیده
The converse statement is also true and is known as the spectral theorem for orthogonal polynomials : if a family of polynomials satisfies a three-term recurrence relation of the form (1.2), with an > 0 and bn ∈ R and initial conditions p0 = 1 and p−1 = 0, then there exists a probability measure μ on the real line such that these polynomials are orthonormal polynomials satisfying (1.1). This gives rise to two important problems: ∗Research supported by INTAS Research Network NeCCA (03-51-6637), FWO projects G.0184.02 and G.0455.04, and OT/04/21 of the Research Counsel of K.U.Leuven.
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