Zero Location and Asymptotic behavior for Extremal Polynomials with Non-Diagonal Sobolev Norms Articles uri icon

publication date

  • December 2010

start page

  • 2225

end page

  • 2242

issue

  • 12

volume

  • 162

international standard serial number (ISSN)

  • 0021-9045

electronic international standard serial number (EISSN)

  • 1096-0430

abstract

  • In this paper we are going to study the zero location and asymptotic behavior of extremal polynomials with respect to a non-diagonal Sobolev norm in the worst case, i.e., when the quadratic form is allowed to
    degenerate. The orthogonal polynomials with respect to this Sobolev norm
    are a particular case of those extremal polynomials. The multiplication
    operator by the independent variable is the main tool in order to
    obtain our results.