Lars-Erik Persson - Böcker

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 Prekopa-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 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 discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis. The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves.

This book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis.The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. Such waves have already been used frequently in the theory of signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing and pattern recognition. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin-Fourier series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group.The first part of the book can be used as an introduction to the subject, and the following chapters summarize the most recent research in this fascinating area and can be read independently. Each chapter concludes with historical remarks and open questions. The book will appeal to researchers working in Fourier and more broad harmonic analysis and will inspire them for their own and their students' research. Moreover, researchers in applied fields will appreciate it as a sourcebook far beyond the traditional mathematical domains.

This third edition presents an expanded and updated treatment of convex analysis methods, incorporating many new results that have emerged in recent years.

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.

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.

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 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.

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.

Boken inleds med ett fylligt kapitel som behandlar geometriska vektorer, linjer och plan samt andragradskurvor. De följande avsnitten som behandlar matriser, linjära avbildningar, linjära ekvationssystem, determinanter samt egenvärden och egenvektorer, bygger i hög grad på detta första kapitel.Två nyskrivna kapitel behandlar basbyten, diagonalisering och kvadratiska former samt ger en inledning till den abstrakta teorin för vektorrum.Boken vänder sig främst till studerande under första året på civilingenjörs- och högskoleingenjörsutbildningar.

Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new fields such as higher order and fractional order Hardy type inequalities and integral inequalities on the cone of monotone functions together with some applications and open problems. The book can serve as a reference and a source of inspiration for researchers working in these and related areas, but could also be used for advanced graduate courses.

Collecting all the results on the particular types of inequalities, the coverage of this book is unique among textbooks in the literature. The book focuses on the historical development of the Carlson inequalities and their many generalizations and variations. As well as almost all known results concerning these inequalities and all known proof techniques, a number of open questions suitable for further research are considered. Two chapters are devoted to clarifying the close connection between interpolation theory and this type of inequality. Other applications are also included, in addition to a historical note on Fritz Carlson himself.

Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy-type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new areas such as higher order and fractional order Hardy-type inequalities and integral inequalities on the cone of monotone functions, together with some applications and open problems.In this second edition, all chapters in the first edition have been updated with new information. Moreover, a new chapter contains new and complementary information concerning: (a) a convexity approach to prove and explain Hardy-type inequalities; (b) sharp constants; (c) scales of inequalities to characterize Hardy-type inequalities; (d) Hardy-type inequalities in other function spaces; and (e) a number of new open questions.