Logarithmic Potential Theory with Applications to Approximation Theory

Details Logarithmic Potential Theory with Applications to Approximation Theory Logarithmic Potential Theory with Applications to Approximation Theory

2010-10-19

arxiv.org/abs/1010.3760v1

Surveys in Approximation Theory, 5 (2010), 165--200

Mathematics

Classical Analysis and ODEs

Scientific paper

We provide an introduction to logarithmic potential theory in the complex plane that particularly emphasizes its usefulness in the theory of polynomial and rational approximation. The reader is invited to explore the notions of Fekete points, logarithmic capacity, and Chebyshev constant through a variety of examples and exercises. Many of the fundamental theorems of potential theory, such as Frostman's theorem, the Riesz Decomposition Theorem, the Principle of Domination, etc., are given along with essential ideas for their proofs. Equilibrium measures and potentials and their connections with Green functions and conformal mappings are presented. Moreover, we discuss extensions of the classical potential theoretic results to the case when an external field is present.

Affiliated with

Also associated with

No associations

Rating

Logarithmic Potential Theory with Applications to Approximation Theory 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 Logarithmic Potential Theory with Applications to Approximation Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Logarithmic Potential Theory with Applications to Approximation Theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-267794