Topics in Uniform Approximation of Continuous Functions

This book presents the evolution of uniform approximations of continuous functions. Starting from the simple case of a real continuous function defined on a closed real interval, i.e., the Weierstrass approximation theorems, it proceeds up to the abstract case of approximation theorems in a locally convex lattice of (M) type. The most important generalizations of Weierstrass' theorems obtained by Korovkin, Bohman, Stone, Bishop, and Von Neumann are also included.

In turn, the book presents the approximation of continuous functions defined on a locally compact space (the functions from a weighted space) and that of continuous differentiable functions defined on ¡n. In closing, it highlights selected approximation theorems in locally convex lattices of (M) type.

The book is intended for advanced and graduate students of mathematics, and can also serve as a resource for researchers in the field of the theory of functions.

Features compact and clearly presented proofs Focuses on approximation theory, providing the key concepts needed to grasp the subject matter Highlighting classic approximation results but also new work, it represents an important contribution to the area of approximation theory

Résumé
"This book is a valuable contribution to the area of uniform approximation of continuous functions. Classical and recent results are presented in a clear, detailed manner. It will be useful for both beginners and experts in this field." ( Ioan Ra a, Mathematical Reviews, June, 2022)

Contenu
Approximation of continuous functions on compact spaces.- Approximation of continuous functions on locally compact spaces.- Approximation of continuous differentiable functions.- Approximations theorems in locally convex lattices.