Logarithmic Potential Theory with Applications to Approximation Theory

By Edward B. Saff. 2010

69 citations recorded by the source corpus.

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. MSC: Primary: 31Cxx, 41Axx

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d0006ed988bd0ad20274010c8308e0d9dbe303c4

Citations in the corpus

• Minimax and maximin space-filling designs: some properties and methods for construction (2017, unknown): “Jourdan and Franco (2009b, 2010) maximise a plug-in estimator of the Shannon entropy H 1 ( ϕ ) = − (cid:82) ϕ ( x ) log ϕ ( x ) d x and estimate ϕ with (Gaussian) kernel smoothing; i.e., their density estimator is where σ n is a bandwidth parameter and ˜ ϕ s 2 is the density of the d -dimensional…”