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Hardy Type Inequalities


Hardy Type Inequalities
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Hardy Type Inequalities


Hardy Type Inequalities
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Author : B. Opic
language : en
Publisher: Longman Scientific and Technical
Release Date : 1990

Hardy Type Inequalities written by B. Opic and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.




The Analysis And Geometry Of Hardy S Inequality


The Analysis And Geometry Of Hardy S Inequality
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Author : Alexander A. Balinsky
language : en
Publisher: Springer
Release Date : 2015-10-20

The Analysis And Geometry Of Hardy S Inequality written by Alexander A. Balinsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-20 with Mathematics categories.


This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.



Weighted Inequalities Of Hardy Type


Weighted Inequalities Of Hardy Type
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Author : Alois Kufner
language : en
Publisher: World Scientific
Release Date : 2003

Weighted Inequalities Of Hardy Type written by Alois Kufner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.


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.



Hardy Type Inequalities On Time Scales


Hardy Type Inequalities On Time Scales
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Author : Ravi P. Agarwal
language : en
Publisher: Springer
Release Date : 2016-10-20

Hardy Type Inequalities On Time Scales written by Ravi P. Agarwal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-20 with Mathematics categories.


The book is devoted to dynamic inequalities of Hardy type and extensions and generalizations via convexity on a time scale T. In particular, the book contains the time scale versions of classical Hardy type inequalities, Hardy and Littlewood type inequalities, Hardy-Knopp type inequalities via convexity, Copson type inequalities, Copson-Beesack type inequalities, Liendeler type inequalities, Levinson type inequalities and Pachpatte type inequalities, Bennett type inequalities, Chan type inequalities, and Hardy type inequalities with two different weight functions. These dynamic inequalities contain the classical continuous and discrete inequalities as special cases when T = R and T = N and can be extended to different types of inequalities on different time scales such as T = hN, h > 0, T = qN for q > 1, etc.In this book the authors followed the history and development of these inequalities. Each section in self-contained and one can see the relationship between the time scale versions of the inequalities and the classical ones. To the best of the authors’ knowledge this is the first book devoted to Hardy-typeinequalities and their extensions on time scales.



Weighted Inequalities Of Hardy Type


Weighted Inequalities Of Hardy Type
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Author : Alois Kufner
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-04-03

Weighted Inequalities Of Hardy Type written by Alois Kufner and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-03 with Mathematics categories.


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.



Hardy Type Inequalities For Abstract Differential Operators


Hardy Type Inequalities For Abstract Differential Operators
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Author : Werner O. Amrein
language : en
Publisher: American Mathematical Soc.
Release Date : 1987

Hardy Type Inequalities For Abstract Differential Operators written by Werner O. Amrein and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.


This paper is concerned with certain estimates on the asymptotic behaviour of the functions [italic]u defined on an interval (a, [infinity symbol]) with values in a Hilbert space [italic]H. More precisely, if [italic]L is a second order ordinary differential operator the coefficients of which are operators acting in [italic]H, we wish to obtain inequalities allowing one to get information about the behaviour of a function [italic]u in a neighborhood of infinity from the asymptotic behaviour of the function [italic]L[italic]u. These inequalities will be called Hardy type inequalities.



Weighted Inequalities Of Hardy Type Second Edition


Weighted Inequalities Of Hardy Type Second Edition
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Author : Lars-erik Persson
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-06-16

Weighted Inequalities Of Hardy Type Second Edition written by Lars-erik Persson and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-16 with Mathematics categories.


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.



Analytical Methods For Markov Semigroups


Analytical Methods For Markov Semigroups
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Author : Luca Lorenzi
language : en
Publisher: CRC Press
Release Date : 2006-07-28

Analytical Methods For Markov Semigroups written by Luca Lorenzi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-28 with Mathematics categories.


For the first time in book form, Analytical Methods for Markov Semigroups provides a comprehensive analysis on Markov semigroups both in spaces of bounded and continuous functions as well as in Lp spaces relevant to the invariant measure of the semigroup. Exploring specific techniques and results, the book collects and updates the literature associated with Markov semigroups. Divided into four parts, the book begins with the general properties of the semigroup in spaces of continuous functions: the existence of solutions to the elliptic and to the parabolic equation, uniqueness properties and counterexamples to uniqueness, and the definition and properties of the weak generator. It also examines properties of the Markov process and the connection with the uniqueness of the solutions. In the second part, the authors consider the replacement of RN with an open and unbounded domain of RN. They also discuss homogeneous Dirichlet and Neumann boundary conditions associated with the operator A. The final chapters analyze degenerate elliptic operators A and offer solutions to the problem. Using analytical methods, this book presents past and present results of Markov semigroups, making it suitable for applications in science, engineering, and economics.



An Invitation To Mathematics


An Invitation To Mathematics
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Author : Dierk Schleicher
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-19

An Invitation To Mathematics written by Dierk Schleicher 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 2011-05-19 with Mathematics categories.


This Invitation to Mathematics consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is about. We hope that it will also be of interest to teachers or more advanced mathematicians who would like to learn about exciting aspects of mathematics outside of their own work or specialization. Together with a team of young ``test readers'', editors and authors have taken great care, through a substantial ``active editing'' process, to make the contributions understandable by the intended readership.



Functional Inequalities New Perspectives And New Applications


Functional Inequalities New Perspectives And New Applications
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Author : Nassif Ghoussoub
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-04-09

Functional Inequalities New Perspectives And New Applications written by Nassif Ghoussoub and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.


"The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website.