Relative Asymptotics of Matrix Orthogonal Polynomials for Uvarov Perturbations: The Degenerate Case Articles uri icon

publication date

  • October 2016

start page

  • 3135

end page

  • 3153

issue

  • 5

volume

  • 13

international standard serial number (ISSN)

  • 1660-5446

electronic international standard serial number (EISSN)

  • 1660-5454

abstract

  • Let be a square matrix of measures, and the associated sequence of orthonormal matrix polynomials satisfying the three-term recurrence relation Let , where is a positive definite matrix, is the Dirac measure supported at that is located outside the support of . We study the outer relative asymptotics of the sequence with respect to the sequence under quite general assumption on the coefficients of the three-term recurrence relation and {B-n (alpha)}(n >= 0).

keywords

  • Outer relative asymptotics; Matrix orthogonal polynomials; Perturbation of a matrix of measures; Unbounded recurrence coefficients; Ratio asymptotics; Gaussian quadrature; Weight matrices; Formulas; Zeros