On the Relevance of Functional Analysis to Economic Theory PDF Download

Author: M. Ali Khan
Publisher:
ISBN:
Category :
Languages : en
Pages : 20

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Author: Yuri Abramovich
Publisher: Springer Science & Business Media
ISBN: 3642722229
Category : Business & Economics
Languages : en
Pages : 301

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In July of 1996, the conference Nonlinear Analysis and its Applications in Engineering and Economics took place on the Greek island of Samos, the birthplace of Pythagoras. During this conference, a special session was held on th the occasion of the 50 birthday of the well known mathematician and math ematical economist Professor Charalambos Aliprantis, who, by his numerous friends, is usually called Roko. The story behind this nickname is not quite clear yet; it will be investigated further and will be made public prior to his th 60 birthday. (At this moment we have already found out that it has nothing to do with the famous movie Rocco and his Brothers even though Roko does have two brothers. ) Roko was born on the Greek island of Cephalonia on May 12,1946, and his elementary and secondary school education took place there. At 18 he entered the Mathematics Department at the University of Athens. Upon graduation from the University of Athens he proceeded with his graduate studies at Cal tech, where in 1973 he completed his Ph. D. degree in Mathematics under the supervision of Professor W. A. J. Luxemburg. His research career can be divided into two periods. The first one, till 1981, was devoted entirely to pure mathematics. The other one, after 1981, has been subdivided between pure mathematics and mathematical economics. The main objects of Roko's work in pure mathematics are spaces with order structure (Riesz spaces) and operators acting on them.

Author: Dean Corbae
Publisher: Princeton University Press
ISBN: 1400833086
Category : Business & Economics
Languages : en
Pages : 696

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Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory

Author: Leonid Vitalʹevich Kantorovich
Publisher: Oxford University Press on Demand
ISBN: 9780195057294
Category : Religion
Languages : en
Pages : 341

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This is a collection of papers on the work of Leonid Kantorovich, a Russian mathematician and economist, and a leading contributor to the fields of optimization and mathematical economics. Kantorovich invented linear programming then applied this theory to optimal macroeconomic planning in a socialist economy, for which he received the Nobel Prize. The book is dedicated to the memory of Kantorovich, who died in 1986. It contains original contributions from several researchers in the USSR never before available in the U.S. It is organized in a logical sequence, from mathematics to the applications of the theories to concrete problems. The work is fully illustrated.

Author: Efe A. Ok
Publisher: Princeton University Press
ISBN: 1400840899
Category : Business & Economics
Languages : en
Pages : 833

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There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students. The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory. The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty. This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory.

Author: Piermarco Cannarsa
Publisher: Springer
ISBN: 3319170198
Category : Mathematics
Languages : en
Pages : 314

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This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two courses, it can be supplemented by additional topics from the third part of the book, such as functions of bounded variation, absolutely continuous functions, and signed measures. This textbook addresses the needs of graduate students in mathematics, who will find the basic material they will need in their future careers, as well as those of researchers, who will appreciate the self-contained exposition which requires no other preliminaries than basic calculus and linear algebra.

Author: Jean-Pierre Aubin
Publisher: Courier Corporation
ISBN: 048646265X
Category : Mathematics
Languages : en
Pages : 658

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Book Description
Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of this text. Both optimization and equilibrium theories are covered in full detail. The book's central application is the fundamental economic problem of allocating scarce resources among competing agents, which leads to considerations of the interrelated applications in game theory and the theory of optimization. Mathematicians, mathematical economists, and operations research specialists will find that it provides a solid foundation in nonlinear functional analysis. This text begins by developing linear and convex analysis in the context of optimization theory. The treatment includes results on the existence and stability of solutions to optimization problems as well as an introduction to duality theory. The second part explores a number of topics in game theory and mathematical economics, including two-person games, which provide the framework to study theorems of nonlinear analysis. The text concludes with an introduction to non-linear analysis and optimal control theory, including an array of fixed point and subjectivity theorems that offer powerful tools in proving existence theorems.

Author: Alampallam V. Balakrishnan
Publisher: Springer Science & Business Media
ISBN: 1461258650
Category : Mathematics
Languages : en
Pages : 385

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In preparing the second edition, I have taken advantage of the opportunity to correct errors as well as revise the presentation in many places. New material has been included, in addition, reflecting relevant recent work. The help of many colleagues (and especially Professor J. Stoer) in ferreting out errors is gratefully acknowledged. I also owe special thanks to Professor v. Sazonov for many discussions on the white noise theory in Chapter 6. February, 1981 A. V. BALAKRISHNAN v Preface to the First Edition The title "Applied Functional Analysis" is intended to be short for "Functional analysis in a Hilbert space and certain of its applications," the applications being drawn mostly from areas variously referred to as system optimization or control systems or systems analysis. One of the signs of the times is a discernible tilt toward application in mathematics and conversely a greater level of mathematical sophistication in the application areas such as economics or system science, both spurred undoubtedly by the heightening pace of digital computer usage. This book is an entry into this twilight zone. The aspects of functional analysis treated here are rapidly becoming essential in the training at the advance graduate level of system scientists and/or mathematical economists. There are of course now available many excellent treatises on functional analysis.

Author:
Publisher:
ISBN: 9780387178332
Category : Functional analysis
Languages : en
Pages : 432

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Author: Mohamed A. El-Hodiri
Publisher: Springer Science & Business Media
ISBN: 3642767931
Category : Business & Economics
Languages : en
Pages : 203

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It is not an exaggeration to state that most problems dealt with in economic theory can be formulated as problems in optimization theory. This holds true for the paradigm of "behavioral" optimization in the pursuit of individual self interests and societally efficient resource allocation, as well as for equilibrium paradigms where existence and stability problems in dynamics can often be stated as "potential" problems in optimization. For this reason, books in mathematical economics and in mathematics for economists devote considerable attention to optimization theory. However, with very few exceptions, the reader who is interested in further study is left with the impression that there is no further place to go to and that what is in these second hand sources is all these is available as far as the subject of optimization theory is concerned. On the other hand the main results from mathematics are often carelessly stated or, more often than not, they do not get to be formally stated at all. Furthermore, it should be well understood that economic theory in general and, mathematical economics in particular, must be classified as special types of applied mathematics or, more precisely, of motivated mathematics since tools of mathematical analysis are used to prove theorems in an economics context in the manner in which probability theory may be classified. Hence, rigor and correct scholarship are of utmost importance and can not be subject to compromise.