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Convex functions play an important role in many branches of mathematics, as well as other areas of science and engineering. The present text is aimed to a thorough introduction to contemporary convex function theory, which entails a powerful and elegant interaction between analysis and geometry. A large variety of subjects are covered, from one real variable case (with all its mathematical gems) to some of the most advanced topics such as the convex calculus, Alexandrov’s Hessian, the variational approach of partial differential equations, the Prékopa-Leindler type inequalities and Choquet's theory. This book can be used for a one-semester graduate course on Convex Functions and Applications, and also as a valuable reference and source of inspiration for researchers working with convexity. The only prerequisites are a background in advanced calculus and linear algebra. Each section ends with exercises, while each chapter ends with comments covering supplementary material and historical information. Many results are new, and the whole book reflects the authors’ own experience, both in teaching and research. About the authors: Constantin P. Niculescu is a Professor in the Department of Mathematics at the University of Craiova, Romania. Dr. Niculescu directs the Centre for Nonlinear Analysis and Its Applications and also the graduate program in Applied Mathematics at Craiova. He received his doctorate from the University of Bucharest in 1974. He published in Banach Space Theory, Convexity Inequalities and Dynamical Systems, and has received several prizes both for research and exposition. Lars Erik Persson is Professor of Mathematics at Luleå University of Technology and Uppsala University, Sweden. He is the director of Center of Applied Mathematics at Luleå, a member of the Swedish National Committee of Mathematics at the Royal Academy of Sciences, and served as President of the Swedish Mathematical Society (1996-1998). He received his doctorate from Umeå University in 1974. Dr. Persson has published on interpolation of operators, Fourier analysis, function theory, inequalities and homogenization theory. He has received several prizes both for research and teaching.

Convex functions --- Convex functions. --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Functions, Convex --- Mathematics. --- Functional analysis. --- Functions of real variables. --- Convex geometry. --- Discrete geometry. --- Real Functions. --- Functional Analysis. --- Convex and Discrete Geometry. --- Functions of real variables --- Discrete groups. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry . --- Real variables --- Functions of complex variables --- Geometry --- Combinatorial geometry

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Inequalities (Mathematics) --- Inégalités (Mathématiques)

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Fourier series. --- Hardy spaces. --- Martingales (Mathematics) --- Sèries de Fourier --- Espais de Hardy --- Martingales (Matemàtica) --- Stochastic processes --- Spaces, Hardy --- Functional analysis --- Functions of complex variables --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Harmonic analysis --- Harmonic functions --- Processos estocàstics --- Hardy, Espacios de --- Anàlisi funcional --- Integrals de Fourier --- Sèries trigonomètriques --- Anàlisi de Fourier --- Càlcul --- Integrals de Dirichlet

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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.

Geometry --- Functional analysis --- Mathematical analysis --- Discrete mathematics --- Mathematics --- Geology. Earth sciences --- analyse (wiskunde) --- discrete wiskunde --- functies (wiskunde) --- wiskunde --- geometrie

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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, 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 mathematics research 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.

Engineering mathematics. --- Mathematical analysis. --- Mathematics. --- Mathematical analysis --- Engineering mathematics --- Engineering & Applied Sciences --- Applied Mathematics --- Engineering --- Engineering analysis --- 517.1 Mathematical analysis --- Mathematics --- Analysis (Mathematics). --- Applied mathematics. --- Applications of Mathematics. --- Appl.Mathematics/Computational Methods of Engineering. --- Signal, Image and Speech Processing. --- Analysis. --- Mathematics Education. --- Study and teaching. --- Math --- Science --- Global analysis (Mathematics). --- Mathematical and Computational Engineering. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Signal processing. --- Image processing. --- Speech processing systems. --- Mathematics—Study and teaching . --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Angewandte Mathematik. --- Lund <2008> --- Engineering—Data processing. --- Mathematics—Study and teaching. --- Mathematical and Computational Engineering Applications. --- Signal, Speech and Image Processing .