Geometric Approximation Theory

This monograph provides a comprehensive introduction to classical geometric approximation theory, emphasizing uniqueness, stability, and existence of elements of best approximation. It discusses the interrelations between main objects and presents auxiliary problems for demonstration. The book covers existence and uniqueness, properties of sets, and approximation by abstract sets, with novel results throughout. It is suitable for both theoretical and applied viewpoints and researchers interested in advanced aspects of the field.

Format: Hardback
Length: 508 pages
Publication date: 29 March 2022
Publisher: Springer Nature Switzerland AG

This comprehensive monograph offers a thorough introduction to classical geometric approximation theory, emphasizing key themes such as uniqueness, stability, and the existence of elements of best approximation. It presents a multitude of fundamental results for both these and related problems, many of which are presented in monograph form for the first time. The text also explores the interconnections between the main objects of geometric approximation theory, formulating a series of auxiliary problems for demonstration. Central ideas encompass the problems of existence and uniqueness of elements of best approximations, as well as properties of sets such as subspaces of polynomials and splines, classes of rational functions, and abstract subsets of normed linear spaces. The book begins with a brief introduction to geometric approximation theory, progressing through fundamental classical ideas and results as a foundation for various approximation sets, suns, and Chebyshev systems. It concludes with a review of approximation by abstract sets and related problems, presenting novel results throughout the section. This text is suitable for both theoretical and applied perspectives, particularly for researchers with an interest in advanced aspects of the field.

Weight: 957g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030909505
Edition number: 1st ed. 2021