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.
- ISBN13 9783030484118
- Publish Date 19 August 2020
- Publish Status Active
- Publish Country CH
- Imprint Springer Nature Switzerland AG
- Edition 1st ed. 2020
- Format Paperback
- Pages 140
- Language English