On second kind polynomials associated with rational transformations of linear functionals

  • Suárez C
  • 1

    Readers

    Mendeley users who have this article in their library.
  • 1

    Citations

    Citations of this article.

Abstract

In this paper the following construction process of orthogonal polynomials on the unit circle is considered: Let u be a regular and hermitian linear functional and let {Φn} be the corresponding orthogonal polynomials sequence. We define a new linear functional L by means the following relation with u:λ (z - β) L = (z - α) u, α, β, λ ∈ C, λ ≠ 0 . In this situation we obtain conditions for the regularity of L, as well as the corresponding orthogonal polynomials sequence. Also, we give one explicit representation for the orthogonal polynomials sequence of the second kind associated to L. For the particular case when α = β, L becomes in the well-known modification of u by addition of a Dirac mass. This case will be studied with special attention. © 2009.

Author-supplied keywords

  • Bernstein-Szegö polynomials
  • Carathéodory function
  • Measure modification
  • Orthogonal polynomials
  • Unit circle

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • C. Suárez

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free