Lars-Erik Persson – författare

Convex functions play an important role in almost all branches of mathematics as well as other areas of science and engineering. This book is a thorough introduction to contemporary convex function theory addressed to all people whose research or teaching interests intersect with the field of convexity. It covers a large variety of subjects, from the one real variable case (with all its mathematical gems) to some of the most advanced topics such as Choquet''s theory, the Prékopa-Leindler type inequalities and their ramifications, as well as the variational approach of partial differential equations and convex programming. Many results are new and the whole book reflects the authors’ own experience, both in teaching and research. The book can serve as a reference and source of inspiration to researchers in several branches of mathematics and engineering and it can also be used for graduate courses.

This third edition presents an expanded and updated treatment of convex analysis methods, incorporating many new results that have emerged in recent years. These additions are essential for grasping the practical applications of convex function theory in solving contemporary real-world problems.

To reflect these advancements, the material has been meticulously reorganized, with a greater emphasis on topics relevant to current research. Additionally, great care has been taken to ensure that the text remains accessible to a broad audience, including both students and researchers focused on the application of mathematics.

Ideal for undergraduate courses, graduate seminars, or as a comprehensive reference, this book is an indispensable resource for those seeking to understand the extensive potential of convex function theory.

This book presents the new fascinating area of continuous inequalities. It was recently discovered that several of the classical inequalities can be generalized and given in a more general continuous/family form. The book states, proves and discusses a number of classical inequalities in such continuous/family forms. Moreover, since many of the classical inequalities hold also in a refined form, it is shown that such refinements can be proven in the more general continuous/family frame.

Written in a pedagogical and reader-friendly way, the book gives clear explanations and examples on how this technique works. The presented interplay between classical theory of inequalities and these newer continuous/family forms, including some corresponding open questions, will appeal to a broad audience of mathematicians and serve as a source of inspiration for further research.

This volume contains 16 refereed research articles on function spaces, interpolation theory and related fields.

Topics covered: theory of function spaces, Hankel-type and related operators, analysis on bounded symmetric domains, partial differential equations, Green functions, special functions, homogenization theory, Sobolev embeddings, Coxeter groups, spectral theory and wavelets.

The book will be of interest to both researchers and graduate students working in interpolation theory, function spaces and operators, partial differential equations and analysis on bounded symmetric domains.

This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some of the most advanced topics.  The new edition includes considerably more material emphasizing the rich applicability of convex analysis to concrete examples.  Chapters 4, 5, and 6 are entirely new, covering important topics such as the Hardy-Littlewood-Pólya-Schur theory of majorization, matrix convexity, and the Legendre-Fenchel-Moreau duality theory.

This book can serve as a reference and source of inspiration to researchers in several branches of mathematics and engineering, and it can also be used as a reference text for graduate courses on convex functions and applications.

This book project was initiated at The Tribute Workshop in Honour of Gunnar Sparr and the follow-up workshop Inequalities, Interpolation, Non-commutative, Analysis, Non-commutative Geometry and Applications INANGA08, held at the Centre for Mathematical Sciences, Lund University in May and November of 2008. 

The resulting book is dedicated in celebration of Gunnar Sparr''s sixty-fifth anniversary and more than forty years of exceptional service to mathematics and its applications in engineering and technology, mathematics and engineering education, as well as interdisciplinary, industrial and international cooperation.  This book presents new advances in several areas of mathematics and engineering mathematics including applications in modern technology, engineering and life sciences.  Thirteen high-quality chapters put forward many new methods and results, reviews of up to date research and open directions and problems for future research. A special chapter by Gunnar Sparr and Georg Lindgren contains a historical account and important aspects of engineering mathematicsresearch and education, and the implementation of the highly successful education programme in Engineering Mathematics at Lund Institute of Technology,  where not only the mathematical sciences have played a role.This book will serve as a source of inspiration for a broad spectrum of researchers and research students.