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