Stieltjes-type Polynomials on the Unit Circle Articles uri icon

publication date

  • June 2009

start page

  • 969

end page

  • 997

issue

  • 266

volume

  • 78

International Standard Serial Number (ISSN)

  • 0025-5718

Electronic International Standard Serial Number (EISSN)

  • 1088-6842

abstract

  • Stieltjes-type polynomials corresponding to measures supported on the unit circle T are introduced and their asymptotic properties away from T are studied for general classes of measures. As an application, we prove the convergence of an associated sequence of interpolating rational functions to the corresponding Carath√©odory function. In turn, this is used to give an estimate of the rate of convergence of certain quadrature formulae that resemble the Gauss-Kronrod rule, provided that the integrand is analytic in a neighborhood of T.