Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations Articles uri icon

publication date

  • January 2023

start page

  • 665

end page

  • 692

issue

  • 1

volume

  • 92

International Standard Serial Number (ISSN)

  • 1017-1398

Electronic International Standard Serial Number (EISSN)

  • 1572-9265

abstract

  • It is well known that Sobolev-type orthogonal polynomials with respect to measures supported on the real line satisfy higher-order recurrence relations and these can be expressed as a (2N + 1)-banded symmetric semi-infinite matrix. In this paper, we state the connection between these (2N + 1)-banded matrices and the Jacobi matrices associated with the three-term recurrence relation satisfied by the standard sequence of orthonormal polynomials with respect to the 2-iterated Christoffel transformation of the measure.

subjects

  • Computer Science
  • Mathematics
  • Physics

keywords

  • five diagonal matrices; jacobi matrices; laguerre polynomials; orthogonal polynomials; recurrence relations; sobolev-type orthogonal polynomials