The Prehistory Of The Theory Of Distributions
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| Author | : J. Lützen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 241 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461394724 |
I first learned the theory of distributions from Professor Ebbe Thue Poulsen in an undergraduate course at Aarhus University. Both his lectures and the textbook, Topological Vector Spaces, Distributions and Kernels by F. Treves, used in the course, opened my eyes to the beauty and abstract simplicity of the theory. However my incomplete study of many branches of classical analysis left me with the question: Why is the theory of distributions important? In my continued studies this question was gradually answered, but my growing interest in the history of mathematics caused me to alter my question to other questions such as: For what purpose, if any, was the theory of distributions originally created? Who invented distributions and when? I quickly found answers to the last two questions: distributions were invented by S. Sobolev and L. Schwartz around 1936 and 1950, respectively. Knowing this answer, however, only created a new question: Did Sobolev and Schwartz construct distributions from scratch or were there earlier trends and, if so, what were they? It is this question, concerning the pre history of the theory of distributions, which I attempt to answer in this book. Most of my research took place at the History of Science Department of Aarhus University. I wish to thank this department for its financial and intellectual support. I am especially grateful to Lektors Kirsti Andersen from the History of Science Department and Lars Mejlbo from the Mathematics Department, for their kindness, constructive criticism, and encouragement.
| Author | : J. Lützen |
| Publisher | : Springer |
| Total Pages | : 232 |
| Release | : 1982-08-02 |
| Genre | : Mathematics |
| ISBN | : 9780387906478 |
I first learned the theory of distributions from Professor Ebbe Thue Poulsen in an undergraduate course at Aarhus University. Both his lectures and the textbook, Topological Vector Spaces, Distributions and Kernels by F. Treves, used in the course, opened my eyes to the beauty and abstract simplicity of the theory. However my incomplete study of many branches of classical analysis left me with the question: Why is the theory of distributions important? In my continued studies this question was gradually answered, but my growing interest in the history of mathematics caused me to alter my question to other questions such as: For what purpose, if any, was the theory of distributions originally created? Who invented distributions and when? I quickly found answers to the last two questions: distributions were invented by S. Sobolev and L. Schwartz around 1936 and 1950, respectively. Knowing this answer, however, only created a new question: Did Sobolev and Schwartz construct distributions from scratch or were there earlier trends and, if so, what were they? It is this question, concerning the pre history of the theory of distributions, which I attempt to answer in this book. Most of my research took place at the History of Science Department of Aarhus University. I wish to thank this department for its financial and intellectual support. I am especially grateful to Lektors Kirsti Andersen from the History of Science Department and Lars Mejlbo from the Mathematics Department, for their kindness, constructive criticism, and encouragement.
| Author | : Paul Walker |
| Publisher | : Routledge |
| Total Pages | : 192 |
| Release | : 2018-05-11 |
| Genre | : Business & Economics |
| ISBN | : 1351041363 |
The theory of the firm did not exist, in any serious manner, until around 1970. Only then did the current theory of the firm literature begin to emerge, based largely upon the work of Ronald Coase and to a lesser degree Frank Knight. It was work by Armen Alchian, Robert Crawford, Harold Demsetz, Michael Jensen, Benjamin Klein, William Meckling and Oliver Williamson, among others, that drove the upswing in interest in the firm among mainstream economists. This accessible book provides a valuable overview of the ‘prehistory’ of the firm. Spanning an impressive timeline, it delves into Antiquity, the Medieval era, the pre-classical economics period and the 19th and 20th centuries. Next, the book traces the theoretical contributions from pre-classical, classical and neoclassical economics. It will be illuminating reading for students and researchers of the history of economic thought, industrial organization, microeconomic theory and business history.
| Author | : Ram P. Kanwal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 490 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 0817681744 |
Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises
| Author | : Ricardo Estrada |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 266 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468400290 |
Asymptotic analysis is an old subject that has found applications in vari ous fields of pure and applied mathematics, physics and engineering. For instance, asymptotic techniques are used to approximate very complicated integral expressions that result from transform analysis. Similarly, the so lutions of differential equations can often be computed with great accuracy by taking the sum of a few terms of the divergent series obtained by the asymptotic calculus. In view of the importance of these methods, many excellent books on this subject are available [19], [21], [27], [67], [90], [91], [102], [113]. An important feature of the theory of asymptotic expansions is that experience and intuition play an important part in it because particular problems are rather individual in nature. Our aim is to present a sys tematic and simplified approach to this theory by the use of distributions (generalized functions). The theory of distributions is another important area of applied mathematics, that has also found many applications in mathematics, physics and engineering. It is only recently, however, that the close ties between asymptotic analysis and the theory of distributions have been studied in detail [15], [43], [44], [84], [92], [112]. As it turns out, generalized functions provide a very appropriate framework for asymptotic analysis, where many analytical operations can be performed, and also pro vide a systematic procedure to assign values to the divergent integrals that often appear in the literature.
| Author | : Vladimir I. Bogachev |
| Publisher | : Springer Nature |
| Total Pages | : 602 |
| Release | : 2020-02-25 |
| Genre | : Mathematics |
| ISBN | : 3030382192 |
This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
| Author | : C.E. Aull |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 416 |
| Release | : 1997-03-31 |
| Genre | : Mathematics |
| ISBN | : 9780792344797 |
This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.
| Author | : Bertram Schefold |
| Publisher | : Taylor & Francis |
| Total Pages | : 463 |
| Release | : 2016-12-01 |
| Genre | : Business & Economics |
| ISBN | : 131731297X |
This is the opus magnum of one of the world’s most renowned experts on the history of economic thought, Bertram Schefold. It contains commentaries from the series Klassiker der Nationalökonomie (Classics of Economics), which have been translated into English for the first time. Schefold’s choices of authors for this series, which he has edited since 1991, and his comments on the various re-edited works, are proof of his highly original and thought-provoking interpretation of the history of economic thought. Together with a companion volume, Great Economic Thinkers from Antiquity to the Historical School: Translations from the series Klassiker der Nationalökonomie, this book is a collection of English translations with introductions by Bertram Schefold. The emphasis of this volume is on the theoretical debates, from the theory of value to imperfect completion; from money to the institutional framework of society; and from the history of economic thought to pioneering works in mathematical economics. This volume is an important contribution to the history of economic thought, not only because it delivers original and fresh insights about well-known figures, such as Marx, Stackelberg, Sraffa, Samuelson, Tooke, Hilferding, Schmoller and Chayanov, but also because it deals with ideas and authors who have been forgotten or neglected in previous literature. This volume is of great interest to those who study the history of economic thought, economic theory and philosophy, as well as those who enjoyed the author’s previous volume, Great Economic Thinkers from Antiquity to the Historical School.
| Author | : Britannica Educational Publishing |
| Publisher | : Britannica Educational Publishing |
| Total Pages | : 311 |
| Release | : 2010-04-01 |
| Genre | : Juvenile Nonfiction |
| ISBN | : 1615302212 |
The field of mathematics today represents an ongoing global effort, spanning both countries and centuries. Through this in-depth narrative, students will learn how major mathematical concepts were first derived, as well as how they evolved with the advent of later thinkers shedding new light on various applications. Everything from Euclidean geometry to the philosophy of mathematics is illuminated as readers are transported to the ancient civilizations of Mesopotamia, Egypt, and beyond to discover the history of mathematical thought
| Author | : Barry Simon |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 811 |
| Release | : 2015-11-02 |
| Genre | : Mathematics |
| ISBN | : 1470410990 |
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.
