High-order recurrence relations, Hermite-Pade approximation and Nikishin systems Articles uri icon

publication date

  • March 2018

start page

  • 385

end page

  • 420

volume

  • 209

international standard serial number (ISSN)

  • 1064-5616

electronic international standard serial number (EISSN)

  • 1468-4802

abstract

  • The study of sequences of polynomials satisfying high-order recurrence relations is connected with the asymptotic behaviour of multiple orthogonal polynomials, the convergence properties of type II Hermite-Pade approximation and eigenvalue distribution of banded Toeplitz matrices. We present some results for the case of recurrences with constant coefficients which match what is known for the Chebyshev polynomials of the first kind. In particular, under appropriate assumptions, we show that the sequence of polynomials satisfies multiple orthogonality relations with respect to a Nikishin-type system of measures.

keywords

  • high-order recurrence relation; Hermite-Pade approximation; multiple orthogonality; Nikishin system