Convergent Interpolation to Cauchy Integrals over Analytic Arcs

Mathematics – Classical Analysis and ODEs

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

We consider multipoint Pad\'e approximation to Cauchy transforms of complex measures. We show that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium distribution of that arc with Dini-smooth non-vanishing density, then the diagonal multipoint Pad\'e approximants associated with appropriate interpolation schemes converge locally uniformly to the approximated Cauchy transform in the complement of the arc. This asymptotic behavior of Pad\'e approximants is deduced from the analysis of underlying non-Hermitian orthogonal polynomials, for which we use classical properties of Hankel and Toeplitz operators on smooth curves. A construction of the appropriate interpolation schemes is explicit granted the parametrization of the arc.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Convergent Interpolation to Cauchy Integrals over Analytic Arcs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Convergent Interpolation to Cauchy Integrals over Analytic Arcs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convergent Interpolation to Cauchy Integrals over Analytic Arcs will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-103672

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.