Continuous Versions Of Some Classical Inequalities

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Continuous Versions Of Some Classical Inequalities

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Author : Ludmila Nikolova
language : en
Publisher: Birkhauser
Release Date : 2025-05-06

Continuous Versions Of Some Classical Inequalities written by Ludmila Nikolova and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-06 with Mathematics categories.

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.

Continuous Versions Of Some Classical Inequalities

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Author : Ludmila Nikolova
language : en
Publisher: Springer Nature
Release Date : 2025-05-28

Continuous Versions Of Some Classical Inequalities written by Ludmila Nikolova and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-28 with Mathematics categories.

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.

Finite Sections Of Some Classical Inequalities

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Author : Herbert S. Wilf
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Finite Sections Of Some Classical Inequalities written by Herbert S. Wilf and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Hardy, Littlewood and P6lya's famous monograph on inequalities [17J has served as an introduction to hard analysis for many mathema ticians. Some of its most interesting results center around Hilbert's inequality and generalizations. This family of inequalities determines the best bound of a family of operators on /p. When such inequalities are restricted only to finitely many variables, we can then ask for the rate at which the bounds of the restrictions approach the uniform bound. In the context of Toeplitz forms, such research was initiated over fifty years ago by Szego [37J, and the chain of ideas continues to grow strongly today, with fundamental contributions having been made by Kac, Widom, de Bruijn, and many others. In this monograph I attempt to draw together these lines of research from the point of view of sharpenings of the classical inequalities of [17]. This viewpoint leads to the exclusion of some material which might belong to a broader-based discussion, such as the elegant work of Baxter, Hirschman and others on the strong Szego limit theorem, and the inclusion of other work, such as that of de Bruijn and his students, which is basically nonlinear, and is therefore in some sense disjoint from the earlier investigations. I am grateful to Professor Halmos for inviting me to prepare this volume, and to Professors John and Olga Todd for several helpful comments. Philadelphia, Pa. H.S.W.

Classical And New Inequalities In Analysis

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Author : Dragoslav S. Mitrinovic
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Classical And New Inequalities In Analysis written by Dragoslav S. Mitrinovic and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

This volume presents a comprehensive compendium of classical and new inequalities as well as some recent extensions to well-known ones. Variations of inequalities ascribed to Abel, Jensen, Cauchy, Chebyshev, Hölder, Minkowski, Stefferson, Gram, Fejér, Jackson, Hardy, Littlewood, Po'lya, Schwarz, Hadamard and a host of others can be found in this volume. The more than 1200 cited references include many from the last ten years which appear in a book for the first time. The 30 chapters are all devoted to inequalities associated with a given classical inequality, or give methods for the derivation of new inequalities. Anyone interested in equalities, from student to professional, will find their favorite inequality and much more.

Tbilisi Analysis And Pde Seminar

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Author : Roland Duduchava
language : en
Publisher: Springer Nature
Release Date : 2024-08-20

Tbilisi Analysis And Pde Seminar written by Roland Duduchava and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-20 with Mathematics categories.

The aim of this volume is to present some new developments and ideas in partial differential equations and mathematical analysis, including spectral analysis and boundary value problems for PDE, harmonic analysis, inequalities, integral equations, and applications. This book is a collection of short summaries of reports from lectures delivered at Tbilisi Analysis & PDE seminars and workshops. In particular, it contains some applications and several open questions aimed at inspiring further research. The volume contains 21 research articles.

Advances In Phase Space Analysis Of Partial Differential Equations

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Author : Antonio Bove
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-18

Advances In Phase Space Analysis Of Partial Differential Equations written by Antonio Bove and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-18 with Mathematics categories.

This collection of original articles and surveys addresses the recent advances in linear and nonlinear aspects of the theory of partial differential equations. The key topics include operators as "sums of squares" of real and complex vector fields, nonlinear evolution equations, local solvability, and hyperbolic questions.

Advances In Directional And Linear Statistics

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Author : Martin T. Wells
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-04

Advances In Directional And Linear Statistics written by Martin T. Wells and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-04 with Mathematics categories.

The present volume consists of papers written by students, colleagues and collaborators of Sreenivasa Rao Jammalamadaka from various countries, and covers a variety of research topics which he enjoys and contributed immensely to.

Convex Functions And Their Applications

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Author : Constantin P. Niculescu
language : en
Publisher: Springer Nature
Release Date : 2025-03-11

Convex Functions And Their Applications written by Constantin P. Niculescu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-11 with Mathematics categories.

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.

Geometry Of Quantum States

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Author : Ingemar Bengtsson
language : en
Publisher: Cambridge University Press
Release Date : 2017-08-18

Geometry Of Quantum States written by Ingemar Bengtsson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-18 with Mathematics categories.

This new edition describes the space of quantum states and the theory of quantum entanglement from a geometric perspective.

The Cauchy Schwarz Master Class

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Author : J. Michael Steele
language : en
Publisher: Cambridge University Press
Release Date : 2004-04-26

The Cauchy Schwarz Master Class written by J. Michael Steele and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-26 with Mathematics categories.

This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.