Asymptotic behaviour of Sobolev orthogonal polynomials on the unit circle Articles uri icon

publication date

  • January 2013

start page

  • 23

end page

  • 38

issue

  • 1

volume

  • 24

international standard serial number (ISSN)

  • 1065-2469

electronic international standard serial number (EISSN)

  • 1476-8291

abstract

  • In this contribution, we deal with analytic properties of sequences of polynomials orthogonal with respect to a Sobolev-type inner product where mu is a non-trivial probability measure supported on the unit circle. We focus our attention on the outer relative asymptotics of these polynomials in terms of those associated with the measure mu. The behaviour of their zeros in terms of the parameter ? is studied in some illustrative examples.

keywords

  • probability measures on the unit circle; orthogonal polynomials; sobolev inner products; outer relative asymptotics; zzeros