A Generalization of Bohr-Mollerup`s Theorem for Higher Order Convex Functions, Marichal
Автор: Marichal Название: A Generalization of Bohr-Mollerup`s Theorem for Higher Order Convex Functions ISBN: 3030950905 ISBN-13(EAN): 9783030950903 Издательство: Springer Рейтинг: Цена: 37260.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic properties of the gamma function using elementary methods of the calculus. Bohr-Mollerup's theorem was then adopted by Nicolas Bourbaki as the starting point for his exposition of the gamma function. This open access book develops a far-reaching generalization of Bohr-Mollerup's theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generalization shows using elementary techniques that a very rich spectrum of functions satisfy analogues of several classical properties of the gamma function, including Bohr-Mollerup's theorem itself, Euler's reflection formula, Gauss' multiplication theorem, Stirling's formula, and Weierstrass' canonical factorization. The scope of the theory developed in this work is illustrated through various examples, ranging from the gamma function itself and its variants and generalizations (q-gamma, polygamma, multiple gamma functions) to important special functions such as the Hurwitz zeta function and the generalized Stieltjes constants. This volume is also an opportunity to honor the 100th anniversary of Bohr-Mollerup's theorem and to spark the interest of a large number of researchers in this beautiful theory.
Автор: Steven G. Krantz; Harold R. Parks Название: The Implicit Function Theorem ISBN: 146145980X ISBN-13(EAN): 9781461459804 Издательство: Springer Рейтинг: Цена: 83850.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: First published in 2003, this is an accessible and thorough treatment of implicit and inverse function theorems and their applications. The book documents and places in context a substantial body of concepts that have played an role in modern mathematics.
Автор: Pfeffer, Washek F. Название: The Divergence Theorem and Sets of Finite Perimeter ISBN: 0367381516 ISBN-13(EAN): 9780367381516 Издательство: Taylor&Francis Рейтинг: Цена: 65320.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This book is devoted to a detailed development of the divergence theorem. The framework is that of Lebesgue integration - no generalized Riemann integrals of Henstock-Kurzweil variety are involved.
In Part I the divergence theorem is established by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral and Hausdorff measures are used. The resulting integration by parts is sufficiently general for many applications. As an example, it is applied to removable singularities of Cauchy-Riemann, Laplace, and minimal surface equations.
The sets of finite perimeter are introduced in Part II. Both the geometric and analytic points of view are presented. The equivalence of these viewpoints is obtained via the functions of bounded variation. These functions are studied in a self-contained manner with no references to Sobolev's spaces. The coarea theorem provides a link between the sets of finite perimeter and functions of bounded variation.
The general divergence theorem for bounded vector fields is proved in Part III. The proof consists of adapting the combinatorial argument of Part I to sets of finite perimeter. The unbounded vector fields and mean divergence are also discussed. The final chapter contains a characterization of the distributions that are equal to the flux of a continuous vector field.
Автор: Simon Barry Название: Loewner`s Theorem on Monotone Matrix Functions ISBN: 3030224244 ISBN-13(EAN): 9783030224240 Издательство: Springer Цена: 102480.00 T Наличие на складе: Поставка под заказ. Описание: This book provides an in depth discussion of Loewner`s theorem on the characterization of matrix monotone functions.
Автор: Simon, Barry Название: Loewner`s theorem on monotone matrix functions ISBN: 303022421X ISBN-13(EAN): 9783030224219 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book provides an in depth discussion of Loewner’s theorem on the characterization of matrix monotone functions. The author refers to the book as a ‘love poem,’ one that highlights a unique mix of algebra and analysis and touches on numerous methods and results. The book details many different topics from analysis, operator theory and algebra, such as divided differences, convexity, positive definiteness, integral representations of function classes, Pick interpolation, rational approximation, orthogonal polynomials, continued fractions, and more. Most applications of Loewner’s theorem involve the easy half of the theorem. A great number of interesting techniques in analysis are the bases for a proof of the hard half. Centered on one theorem, eleven proofs are discussed, both for the study of their own approach to the proof and as a starting point for discussing a variety of tools in analysis. Historical background and inclusion of pictures of some of the main figures who have developed the subject, adds another depth of perspective.
The presentation is suitable for detailed study, for quick review or reference to the various methods that are presented. The book is also suitable for independent study. The volume will be of interest to research mathematicians, physicists, and graduate students working in matrix theory and approximation, as well as to analysts and mathematical physicists.
Автор: Huan-nan Shi Название: Schur-Convex Functions and Inequalities: Volume 2: Applications in Inequalities ISBN: 3110606577 ISBN-13(EAN): 9783110606577 Издательство: Walter de Gruyter Рейтинг: Цена: 149940.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This two-volume work introduces the theory and applications of Schur-convex functions. The second volume mainly focuses on the application of Schur-convex functions in sequences inequalities, integral inequalities, mean value inequalities for two variables, mean value inequalities for multi-variables, and in geometric inequalities.
Автор: Robert R. Phelps Название: Convex Functions, Monotone Operators and Differentiability ISBN: 3540567151 ISBN-13(EAN): 9783540567158 Издательство: Springer Рейтинг: Цена: 23280.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Starting with convex functions on the line, this title leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational principles and perturbed optimization.
Автор: Huan-nan Shi Название: Schur-Convex Functions and Inequalities: Volume 1: Concepts, Properties, and Applications in Symmetric Function Inequalities ISBN: 3110606127 ISBN-13(EAN): 9783110606126 Издательство: Walter de Gruyter Рейтинг: Цена: 149940.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This two-volume work introduces the theory and applications of Schur-convex functions. The first volume introduces concepts and properties of Schur-convex functions, including Schur-geometrically convex functions, Schur-harmonically convex functions, Schur-power convex functions, etc. and also discusses applications of Schur-convex functions in symmetric function inequalities.
Автор: D. Butnariu; A.N. Iusem Название: Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization ISBN: 9401057885 ISBN-13(EAN): 9789401057882 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The aim of this work is to present in a unified approach a series of results concerning totally convex functions on Banach spaces and their applications to building iterative algorithms for computing common fixed points of mea- surable families of operators and optimization methods in infinite dimen- sional settings.
Автор: Constantin P. Niculescu; Lars-Erik Persson Название: Convex Functions and Their Applications ISBN: 3030086798 ISBN-13(EAN): 9783030086794 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 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-P?lya-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.
Автор: Chongchun Zeng, Zhiwu Lin Название: Instability, Index Theorem, and Exponential Trichotomy for Linear Hamiltonian PDEs ISBN: 1470450445 ISBN-13(EAN): 9781470450441 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 84090.00 T Наличие на складе: Нет в наличии. Описание: This book presents an overview of the diverse literature on change-point methodology and describes some unifying themes and recent breakthroughs. It can be used as a second-year Ph.D. level course in statistics. It is expected to be useful to researchers and graduate students, not only in statistics but also in engineering, biomedicine, economics and finance.
Автор: V. Paulauskas; A. Rackauskas Название: Approximation Theory in the Central Limit Theorem ISBN: 9401178003 ISBN-13(EAN): 9789401178006 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ.
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