A canonical family of multiple orthogonal polynomials for Nikishin systems

[摘要] For any pair of compact intervals of the real line Delta(1), Delta(2), with Delta(1) boolean AND Delta(2) = empty set, we obtain two probability measures mu(1), tau(1), supported on Delta(1) and Delta(2) respectively, such that the Nikishin system. N(mu(1), tau(1)) has a sequence of monic multiple orthogonal polynomials which satisfy a four term recurrence relation with constant coefficients of period 2. The measures are obtained from the functions which give the ratio asymptotic of multiple orthogonal polynomials with respect to an arbitrary Nikishin system. N(sigma(1), sigma(2)) on Delta(1), Delta(2), such that sigma(i)' > 0 a.e. on Delta(i), i = 1,2. The role of mu(1), tau(1) is symmetric in the sense that the same construction is possible on Delta(2), Delta(1), with N(tau(1), mu(1)). (C) 2010 Published by Elsevier Inc.

[发布日期] 2010-12-15

[关键词] Hermite-Pade orthogonal polynomials;Multiple orthogonal polynomials;Nikishin system;Varying measures;Ratio asymptotic