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 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir describes a new way of looking at the classical inequalities. The most famous such results, (those of Hilbert, Hardy, and Copson) may be interpreted as inclusion relationships, l[superscript italic]p [subset equality symbol] [italic capital]Y, between certain (Banach) sequence spaces, the norm of the injection being the best constant of the particular inequality. The inequalities of Hilbert, Hardy, and Copson all share the same space [italic capital]Y. That space -- alias [italic]ces([italic]p) -- is central to many celebrated inequalities, and thus is studied here in considerable detail.
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 309 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 Weighted Inequalities Of Hardy Type Second Edition written by Lars-erik Persson 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.
Download or read book Weighted Inequalities of Hardy Type written by Alois Kufner and published by World Scientific. This book was released on 2003 with total page 380 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 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.
Download or read book The Blocking Technique Weighted Mean Operators and Hardy s Inequality written by Karl-Goswin Grosse-Erdmann and published by Springer Science & Business Media. This book was released on 1998-01-19 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the first comprehensive treatment of the blocking technique which consists in transforming norms in section form into norms in block form, and vice versa. Such norms appear throughout analysis. The blocking technique is a powerful, yet elementary, tool whose usefulnes is demonstrated in the book. In particular, it is shown to lead to the solution of three recent problems of Bennett concerning the inequalities of Hardy and Copson. The book is addressed to researchers and graduate students. An interesting feature is that it contains a dictionary of transformations between section and block norms and will thus be useful to researchers as a reference text. The book requires no knowledge beyond an introductory course in functional analysis.
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.
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.
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.
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 469 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.
Download or read book Integral Operators in Non Standard Function Spaces written by Vakhtang Kokilashvili and published by Springer Nature. This book was released on with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Progress in Function Theory and Operator Theory written by Alberto A. Condori and published by American Mathematical Society. This book was released on 2024-04-30 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Recent Progress in Function Theory and Operator Theory, held virtually on April 6, 2022. Function theory is a classical subject that examines the properties of individual elements in a function space, while operator theory usually deals with concrete operators acting on such spaces or other structured collections of functions. These topics occupy a central position in analysis, with important connections to partial differential equations, spectral theory, approximation theory, and several complex variables. With the aid of certain canonical representations or “models”, the study of general operators can often be reduced to that of the operator of multiplication by one or several independent variables, acting on spaces of analytic functions or compressions of this operator to co-invariant subspaces. In this way, a detailed understanding of operators becomes connected with natural questions concerning analytic functions, such as zero sets, constructions of functions constrained by norms or interpolation, multiplicative structures granted by factorizations in spaces of analytic functions, and so forth. In many cases, non-obvious problems initially motivated by operator-theoretic considerations turn out to be interesting on their own, leading to unexpected challenges in function theory. The research papers in this volume deal with the interplay between function theory and operator theory and the way in which they influence each other.
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.
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.
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.
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 302 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.
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 328 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.
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 97 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 analysed.
