Uniform Approximation and Fine Potential Theory

Weierstrass and Uniform Approximation

We present the theorem of uniform approximation of continuous functions by polynomials in the Weierstrass framework for the construction of analysis based on the representation of functions by sums of power series and analytic functions, and his effort to bring new standards of rigor to analysis that accompanied his differences with Riemann. We also describe the most original proofs of the appr...

fragmentability and approximation

in chapter 1, charactrizations of fragmentability, which are obtained by namioka (37), ribarska (45) and kenderov-moors (32), are given. also the connection between fragmentability and its variants and other topics in banach spaces such as analytic space, the radone-nikodym property, differentiability of convex functions, kadec renorming are discussed. in chapter 2, we use game characterization...

Metric–fine uniform frames

A locallic version of Hager’s metric-fine spaces is presented. A general definition of A-fineness is given and various special cases are considered, notably A = all metric frames, A = complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed.

Logarithmic Potential Theory with Applications to Approximation Theory

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 Fr...

On Constrained Uniform Approximation