Overview
- 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
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (4 chapters)
Keywords
About this book
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.
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Authors and Affiliations
Bibliographic Information
Book Title: Topics in Uniform Approximation of Continuous Functions
Authors: Ileana Bucur, Gavriil Paltineanu
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/978-3-030-48412-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-48411-8Published: 19 August 2020
eBook ISBN: 978-3-030-48412-5Published: 18 August 2020
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: X, 140
Number of Illustrations: 1 illustrations in colour
Topics: Functional Analysis