Geometry of the Unit Sphere in Polynomial Spaces

Geometry of the Unit Sphere in Polynomial Spaces

 
Edition number: 1st ed. 2022
Publisher: Springer
Date of Publication:
Number of Volumes: 1 pieces, Book
 
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Product details:

ISBN13:9783031236754
ISBN10:30312367511
Binding:Paperback
No. of pages:137 pages
Size:235x155 mm
Weight:232 g
Language:English
Illustrations: 41 Illustrations, black & white
595
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Long description:

This brief presents a global perspective on the geometry of spaces of polynomials. Its particular focus is on polynomial spaces of dimension 3, providing, in that case, a graphical representation of the unit ball. Also, the extreme points in the unit ball of several polynomial spaces are characterized. Finally, a number of applications to obtain sharp classical polynomial inequalities are presented.

The study performed is the first ever complete account on the geometry of the unit ball of polynomial spaces. Nowadays there are hundreds of research papers on this topic and our work gathers the state of the art of the main and/or relevant results up to now. This book is intended for a broad audience, including undergraduate and graduate students, junior and senior researchers and it also serves as a source book for consultation. In addition to that, we made this work visually attractive by including in it over 50 original figures in order to help in the understanding of all the results and techniques included in the book.


Table of Contents:
Chapter. 1. Introduction
Chapter. 2. Polynomials of degree
Chapter. 3. Spaces of trinomials
Chapter. 4. Polynomials on nonsymmetric convex bodies
Chapter. 5. Sequence Banach spaces
Chapter. 6. Polynomials with the hexagonal and octagonal norms
Chapter. 7. Hilbert spaces
Chapter. 8. Banach spaces
Chapter. 9. Applications