Domingo García - Böcker

Convex Analysis in Polynomial Spaces with Applications is intended to serve a broad audience of undergraduate and graduate students, junior and senior researchers, and as a general self-study guide for anyone who wishes to get acquainted with the geometry of Banach spaces of polynomials with applications. This text is specifically designed to be appealing and accessible to the reader and provides a general overview on the topic together with new and interesting directions of research. The text also contains original results and material never published before.Features Comprehensive review on the geometry of spaces of polynomials. Visually attractive and accessible presentation, with over 75 explanatory figures. Contains many examples illustrating the results and techniques appearing in the book. Open (and deep!) questions within the area are provided so that the interested reader can begin doing independent research using the techniques presented in the text. It also features original results by the authors.

This brief presents a global perspective on the geometry of spaces of polynomials. 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.