Weighted Extremal Domains and Best Rational Approximation

Details Weighted Extremal Domains and Best Rational Approximation Weighted Extremal Domains and Best Rational Approximation

2011-08-22

arxiv.org/abs/1108.4363v1

Adv. Math. 229, 357-407, 2012

Mathematics

Classical Analysis and ODEs

44 pages, 5 figures

Scientific paper

Let f be holomorphically continuable over the complex plane except for finitely many branch points contained in the unit disk. We prove that best rational approximants to f of degree n, in the L^2-sense on the unit circle, have poles that asymptotically distribute according to the equilibrium measure on the compact set outside of which f is single-valued and which has minimal Green capacity in the disk among all such sets. This provides us with n-th root asymptotics of the approximation error. By conformal mapping, we deduce further estimates in approximation by rational or meromorphic functions to f in the L^2-sense on more general Jordan curves encompassing the branch points. The key to these approximation-theoretic results is a characterization of extremal domains of holomorphy for f in the sense of a weighted logarithmic potential, which is the technical core of the paper.

Affiliated with

Also associated with

No associations

Rating

Weighted Extremal Domains and Best Rational Approximation 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 Weighted Extremal Domains and Best Rational Approximation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weighted Extremal Domains and Best Rational Approximation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-176635