A canonical family of multiple orthogonal polynomials for Nikishin systems

For any pair of compact intervals of the real line Δ 1 , Δ 2 , with Δ 1 ∩ Δ 2 = ∅ , we obtain two probability measures μ 1 , τ 1 , supported on Δ 1 and Δ 2 respectively, such that the Nikishin system N ( μ 1 , τ 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 ( σ 1 , σ 2 ) on Δ 1 , Δ 2 , such that σ i ′ > 0 a.e. on Δ i , i = 1 , 2 . The role of μ 1 , τ 1 is symmetric in the sense that the same construction is possible on Δ 2 , Δ 1 , with N ( τ 1 , μ 1 ) .