Vector Interpretation of the Matrix Orthogonality on the Real Line Articles uri icon

publication date

  • December 2010

start page

  • 357

end page

  • 383

issue

  • 3

volume

  • 112

international standard serial number (ISSN)

  • 0167-8019

electronic international standard serial number (EISSN)

  • 1572-9036

abstract

  • In this paper we study sequences of vector orthogonal polynomials. The vector orthogonality presented here provides a reinterpretation of what is known in the literature as matrix orthogonality. These systems of
    orthogonal polynomials satisfy three-term recurrence relations with
    matrix coefficients that do not obey to any type of symmetry. In this
    sense the vectorial reinterpretation allows us to study a non-symmetric
    case of the matrix orthogonality. We also prove that our systems of
    polynomials are indeed orthonormal with respect to a complex measure of
    orthogonality. Approximation problems of Hermite-Padé type are also
    discussed. Finally, a Markov's type theorem is presented.