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

Autorentext
Dr. Gavriil Paltineanu was a professor in the Department of Mathematics and Computer Science, Technical University of Civil Engineering of Bucharest, and he was a member of editorial board in Mathematical Reports of Romanian Academy. His research interests are approximation theory, real analysis, and convexity. And he published 56 research papers, 4 monographs, 13 books, and 5 exercise books for students during his career. Dr. Ileana Gabriela Bucur is an associated professor in the Department of Mathematics and Computer Science at the Civil Engineering faculty, Bucharest, Romania. She received her Ph.D. degree from University of Bucharest, in 1996. Her researches include knowledge in general topology, topological vector-ordered spaces, functional analysis, real analysis, approximation theory. Dr. Mariana Zamfir is an assistant professor in the Department of Mathematics and Computer Science of Technical University of Civil Engineering Bucharest, Romania.She received her Ph.D. degree in Mathematics at University of Bucharest, Romania, in 2012. Her fields of research include knowledge in spectral theory of operators, representations of Hilbert C-modules and C-algebras, projective representations, completely positive linear maps.

Inhalt

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.