Manuel Maestre - 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.

Over 100 years ago Harald Bohr identified a deep problem about the convergence of Dirichlet series, and introduced an ingenious idea relating Dirichlet series and holomorphic functions in high dimensions. Elaborating on this work, almost twnety years later Bohnenblust and Hille solved the problem posed by Bohr. In recent years there has been a substantial revival of interest in the research area opened up by these early contributions. This involves the intertwining of the classical work with modern functional analysis, harmonic analysis, infinite dimensional holomorphy and probability theory as well as analytic number theory. New challenging research problems have crystallized and been solved in recent decades. The goal of this book is to describe in detail some of the key elements of this new research area to a wide audience. The approach is based on three pillars: Dirichlet series, infinite dimensional holomorphy and harmonic analysis.

The aim of this book is to facilitate the use of Stokes' Theorem in applications.  The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three variables.  Several practical methods and many solved exercises are provided. This book tries to show that vector analysis and vector calculus are not always at odds with one another.  Key topics include:-vectors and vector fields;-line integrals;-regular k-surfaces;-flux of a vector field;-orientation of a surface;-differential forms;-Stokes' theorem;-divergence theorem. This book is intended for upper undergraduate students who have completed a standard introduction to differential and integral calculus for functions of several variables.  The book can also be useful to engineering and physicsstudents who know how to handle the theorems of Green, Stokes and Gauss, but would like to explore the topic further.