Direct spectral problem for multiple orthogonal polynomials defined by higher order three term recurrences

Problem of approximation of measures of orthogonality for multiple orthogonal polynomials is considered. For a class of multiple orthogonal polynomials defined by higher order three term recurrences a uniform approximation of the weight functions inside the common support of measures is obtained. This approximation involves a new Turan like determinants associated with multiple orthogonal polynomials.