A canonical family of multiple orthogonal polynomials for Nikishin systems

For any pair of compact intervals of the real line Δ1, Δ2, with Δ1∩Δ2=∅, we obtain two probability measures μ1, τ1, supported on Δ1 and Δ2 respectively, such that the Nikishin system N(μ1,τ1) 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(σ1,σ2) on Δ1, Δ2, such that a.e. on Δi, i=1,2. The role of μ1, τ1 is symmetric in the sense that the same construction is possible on Δ2, Δ1, with N(τ1,μ1).