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Factorizing The Classical Inequalities
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Book Synopsis Factorizing the Classical Inequalities by : Grahame Bennett
Download or read book Factorizing the Classical Inequalities written by Grahame Bennett and published by American Mathematical Soc.. This book was released on 1996 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes a new way of looking at the classical inequalities. The most famous such results (Hilbert, Hardy, and Copson) may be interpreted as inclusion relationships, $l^p\subseteq Y$, between certain (Banach) sequence spaces, the norm of the injection being the best constant of the particular inequality. The authors' approach is to replace $l^p$ by a larger space, $X$, with the properties: $\Vert l^p\subseteq X\Vert =1$ and $\Vert X\subseteq Y\Vert =\Vert l^p\subseteq Y\Vert$, the norm on $X$ being so designed that the former property is intuitive. Any such result constitutes an enhancement of the original inequality, because you now have the classical estimate, $\Vert l^p\subseteq Y\Vert$, holding for a larger collection, $X=Y$. The authors' analysis has some noteworthy features: The inequalities of Hilbert, Hardy, and Copson (and others) all share the same space $Y$. That space-alias ces($p$ )-being central to so many celebrated inequalities, the authors conclude, must surely be important. It is studied here in considerable detail. The renorming of $Y$ is based upon a simple factorization, $Y= l^p\cdot Z$ (coordinatewise products), wherein $Z$ is described explicitly. That there is indeed a renorming, however, is not so simple. It is proved only after much preparation when duality theory is considered.
Book Synopsis Weighted Inequalities of Hardy Type by : Alois Kufner
Download or read book Weighted Inequalities of Hardy Type written by Alois Kufner and published by World Scientific Publishing Company. This book was released on 2017-06-16 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Request Inspection Copy
Book Synopsis The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities by : George Xian-Zhi Yuan
Download or read book The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities written by George Xian-Zhi Yuan and published by American Mathematical Soc.. This book was released on 1998 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given.
Book Synopsis Some Connections between Isoperimetric and Sobolev-type Inequalities by : Serguei Germanovich Bobkov
Download or read book Some Connections between Isoperimetric and Sobolev-type Inequalities written by Serguei Germanovich Bobkov and published by American Mathematical Soc.. This book was released on 1997 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: For Borel probability measures on metric spaces, this text studies the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the isoperimetric problem and the validity of some analytic inequalities. The book devotes much attention to: the probability distributions on the real line; the normalized Lebesgue measure on the Euclidean sheres; and the canonical Gaussian measure on the Euclidean space.
Book Synopsis Survey on Classical Inequalities by : Themistocles RASSIAS
Download or read book Survey on Classical Inequalities written by Themistocles RASSIAS and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Survey on Classical Inequalities provides a study of some of the well known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy-Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, Shannon's and related inequalities, generalized Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted Lp -norm inequalities in convolutions, inequalities for polynomial zeros as well as applications in a number of problems of pure and applied mathematics. It is my pleasure to express my appreciation to the distinguished mathematicians who contributed to this volume. Finally, we wish to acknowledge the superb assistance provided by the staff of Kluwer Academic Publishers. June 2000 Themistocles M. Rassias Vll LYAPUNOV INEQUALITIES AND THEIR APPLICATIONS RICHARD C. BROWN Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA. email address:[email protected] DON B. HINTON Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA. email address: [email protected] Abstract. For nearly 50 years Lyapunov inequalities have been an important tool in the study of differential equations. In this survey, building on an excellent 1991 historical survey by Cheng, we sketch some new developments in the theory of Lyapunov inequalities and present some recent disconjugacy results relating to second and higher order differential equations as well as Hamiltonian systems. 1. Introduction Lyapunov's inequality has proved useful in the study of spectral properties of ordinary differential equations. Typical applications include bounds for eigenvalues, stability criteria for periodic differential equations, and estimates for intervals of disconjugacy.
Book Synopsis Advances in Mathematical Analysis and its Applications by : Bipan Hazarika
Download or read book Advances in Mathematical Analysis and its Applications written by Bipan Hazarika and published by CRC Press. This book was released on 2022-12-12 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Mathematical Analysis and its Applications is designed as a reference text and explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. It discusses theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some topics are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. Features: The book encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. It offers an understanding of research problems by presenting the necessary developments in reasonable details The book also discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problems Contains applications on wavelets analysis and COVID-19 to show that mathematical analysis has interdisciplinary as well as real life applications. The book is aimed primarily at advanced undergraduates and postgraduate students studying mathematical analysis and mathematics in general. Researchers will also find this book useful.
Book Synopsis Mathematics and Computing by : Debdas Ghosh
Download or read book Mathematics and Computing written by Debdas Ghosh and published by Springer. This book was released on 2018-09-28 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses recent advances and research in applied mathematics, statistics and their applications in computing. It features papers presented at the fourth conference in the series organized at the Indian Institute of Technology (Banaras Hindu University), Varanasi, India, on 9 – 11 January 2018 on areas of current interest, including operations research, soft computing, applied mathematical modelling, cryptology, and security analysis. The conference has emerged as a powerful forum, bringing together leading academic scientists, experts from industry, and researchers and offering a venue to discuss, interact and collaborate to stimulate the advancement of mathematics and its applications in computer science. The education of future consumers, users, producers, developers and researchers of mathematics and its applications is an important challenge in modern society, and as such, mathematics and its application in computer science are of vital significance to all spectrums of the community, as well as to mathematicians and computing professionals across different educational levels and disciplines. With contributions by leading international experts, this book motivates and creates interest among young researchers.
Book Synopsis Hardy Type Inequalities on Time Scales by : Ravi P. Agarwal
Download or read book Hardy Type Inequalities on Time Scales written by Ravi P. Agarwal and published by Springer. This book was released on 2016-10-20 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Theory written by Steven Lord and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-07-19 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the fundamental approach provided by Albrecht Pietsch. For mathematical physicists and other users of Connes’ noncommutative geometry the text offers a complete reference to traces on weak trace class operators, including Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions.
Book Synopsis Optimal Domain and Integral Extension of Operators by : S. Okada
Download or read book Optimal Domain and Integral Extension of Operators written by S. Okada and published by Springer Science & Business Media. This book was released on 2008-09-09 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator. Most of the material appears in print for the first time. The book has an interdisciplinary character and is aimed at graduates, postgraduates, and researchers in modern operator theory.
Book Synopsis Approximation Theory, Sequence Spaces and Applications by : S. A. Mohiuddine
Download or read book Approximation Theory, Sequence Spaces and Applications written by S. A. Mohiuddine and published by Springer Nature. This book was released on 2022-12-07 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance and summarizes ways of their solution and possible applications which improve the current understanding pertaining to sequence spaces and approximation theory. The presentation of the articles is clear and self-contained throughout the book.
Book Synopsis Asymptotic Completeness, Global Existence and the Infrared Problem for the Maxwell-Dirac Equations by : Moshé Flato
Download or read book Asymptotic Completeness, Global Existence and the Infrared Problem for the Maxwell-Dirac Equations written by Moshé Flato and published by American Mathematical Soc.. This book was released on 1997 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this work is to present and give full proofs of new original research results concerning integration of and scattering for the classical Maxwell-Dirac equations. These equations govern first quantized electrodynamics and are the starting point for a rigorous formulation of quantum electrodynamics. The presentation is given within the formalism of nonlinear group and Lie algebra representations, i.e. the powerful new approach to nonlinear evolution equations covariant under a group action. The authors prove that the nonlinear Lie algebra representation given by the manifestly covariant Maxwell-Dirac equations is integrable to a global nonlinear representation of the Poincare group on a differentiable manifold of small initial conditions. This solves, in particular, the small-data Cauchy problem for the Maxwell-Dirac equations globally in time. The existence of modified wave operators and asymptotic completeness is proved. The asymptotic representations (at infinite time) turn out to be nonlinear. A cohomological interpretation of the results in the spirit of nonlinear representation theory and its connection to the infrared tail of the electron are developed.
Book Synopsis Descriptive Topology and Functional Analysis II by : Juan Carlos Ferrando
Download or read book Descriptive Topology and Functional Analysis II written by Juan Carlos Ferrando and published by Springer. This book was released on 2019-06-02 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of a meeting on Topology and Functional Analysis, and is dedicated to Professor Manuel López-Pellicer's mathematical research. Covering topics in descriptive topology and functional analysis, including topological groups and Banach space theory, fuzzy topology, differentiability and renorming, tensor products of Banach spaces and aspects of Cp-theory, this volume is particularly useful to young researchers wanting to learn about the latest developments in these areas.
Book Synopsis Time-Dependent Subdifferential Evolution Inclusions and Optimal Control by : Shouchuan Hu
Download or read book Time-Dependent Subdifferential Evolution Inclusions and Optimal Control written by Shouchuan Hu and published by American Mathematical Soc.. This book was released on 1998 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume studies multivalued evolution equations driven by time-dependent subdifferential operators and optimal control problems for such systems. The formulation is general enough to incorporate problems with time varying constraints. For evolution inclusions, existence relaxation and structural results for the solution set are proved. For optimal control problems, a general existence theory is developed, different forms of the relaxed problem are introduced and studied, well-posedness properties are investigated and the precise relation between the properties of relaxability and well-posedness is established. Various examples of systems which fit in the abstract framework are analyzed.
Book Synopsis Abelian Galois Cohomology of Reductive Groups by : Mikhail Borovoi
Download or read book Abelian Galois Cohomology of Reductive Groups written by Mikhail Borovoi and published by American Mathematical Soc.. This book was released on 1998 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, a new functor $H^2_{ab}(K,G)$ of abelian Galois cohomology is introduced from the category of connected reductive groups $G$ over a field $K$ of characteristic $0$ to the category of abelian groups. The abelian Galois cohomology and the abelianization map$ab^1:H^1(K,G) \rightarrow H^2_{ab}(K,G)$ are used to give a functorial, almost explicit description of the usual Galois cohomology set $H^1(K,G)$ when $K$ is a number field.
Book Synopsis Orders of a Quartic Field by : Jin Nakagawa
Download or read book Orders of a Quartic Field written by Jin Nakagawa and published by American Mathematical Soc.. This book was released on 1996 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the author studies the Dirichlet series whose coefficients are the number of orders of a quartic field with given indices. Nakagawa gives an explicit expression of the Dirichlet series. Using this expression, its analytic properties are deduced. He also presents an asymptotic formula for the number of orders in a quartic field with index less than a given positive number.
Book Synopsis The Fundamental Lemma for the Shalika Subgroup of $GL(4)$ by : Solomon Friedberg
Download or read book The Fundamental Lemma for the Shalika Subgroup of $GL(4)$ written by Solomon Friedberg and published by American Mathematical Soc.. This book was released on 1996 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors establish the fundamental lemma for a relative trace formula. The trace formula compares generic automorphic representations of [italic capitals]GS[italic]p(4) with automorphic representations of [italic capitals]GS(4) which are distinguished with respect to a character of the Shalika subgroup, the subgroup of matrices of 2 x 2 block form ([superscript italic]g [over] [subscript capital italic]X [and] 0 [over] [superscript italic]g). The fundamental lemma, giving the equality of the orbital integrals of the unit elements of the respective Hecke algebras, amounts to a comparison of certain exponential sums arising from these two different groups.
