Geometry of the unit sphere in polynomial spaces
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Bibliographic Information
Geometry of the unit sphere in polynomial spaces
（SpringerBriefs in mathematics）
Springer, 2022
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Includes bibliographical references
Description and Table of Contents
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. IntroductionChapter. 2. Polynomials of degreeChapter. 3. Spaces of trinomialsChapter. 4. Polynomials on nonsymmetric convex bodiesChapter. 5. Sequence Banach spacesChapter. 6. Polynomials with the hexagonal and octagonal normsChapter. 7. Hilbert spacesChapter. 8. Banach spacesChapter. 9. Applications
by "Nielsen BookData"
