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The Theory Of Distributions
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Book Synopsis Introduction to the Theory of Distributions by : F. G. Friedlander
Download or read book Introduction to the Theory of Distributions written by F. G. Friedlander and published by Cambridge University Press. This book was released on 1998 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of a classic graduate text on the theory of distributions.
Book Synopsis Theory of Distributions by : Svetlin G. Georgiev
Download or read book Theory of Distributions written by Svetlin G. Georgiev and published by Springer. This book was released on 2015-07-13 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.
Book Synopsis The Theory of Distributions by : J. Ian Richards
Download or read book The Theory of Distributions written by J. Ian Richards and published by CUP Archive. This book was released on 1995-09-29 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained mathematical introduction that concentrates on the essential results important to non-specialists.
Download or read book Distributions written by J.J. Duistermaat and published by Springer Science & Business Media. This book was released on 2010-08-09 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.
Book Synopsis Distribution Theory and Transform Analysis by : A.H. Zemanian
Download or read book Distribution Theory and Transform Analysis written by A.H. Zemanian and published by Courier Corporation. This book was released on 2011-11-30 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.
Book Synopsis A Guide to Distribution Theory and Fourier Transforms by : Robert S. Strichartz
Download or read book A Guide to Distribution Theory and Fourier Transforms written by Robert S. Strichartz and published by World Scientific. This book was released on 2003 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.
Book Synopsis The Prehistory of the Theory of Distributions by : J. Lützen
Download or read book The Prehistory of the Theory of Distributions written by J. Lützen and published by Springer. This book was released on 1982-08-02 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Distributions by : M.A. Al-Gwaiz
Download or read book Theory of Distributions written by M.A. Al-Gwaiz and published by CRC Press. This book was released on 1992-04-24 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook for a graduate course in the theory of distributions and related topics, for students of applied mathematics or theoretical physics. Introduces the theory, explicates mathematical structures and the Hilbert-space aspects, and presents applications to typical boundary problems. Annotation
Book Synopsis Distributions and Operators by : Gerd Grubb
Download or read book Distributions and Operators written by Gerd Grubb and published by Springer Science & Business Media. This book was released on 2008-10-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises and examples.
Book Synopsis Introduction to the Theory of Distributions by : Israel Halperin
Download or read book Introduction to the Theory of Distributions written by Israel Halperin and published by . This book was released on 1952 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This pamphlet, based on lectures given by Laurent Schwartz at the Canadian Mathematical Congress in 1951, gives a detailed introduction to the theory of distributions, in terms of classical analysis, for applied mathematicians and physicists. Mathematical Congress Lecture Series, No. 1
Book Synopsis Multiplication of Distributions by : Jean F. Colombeau
Download or read book Multiplication of Distributions written by Jean F. Colombeau and published by Springer. This book was released on 2006-11-15 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent and very elementary developments of a theory of multiplication of distributions in the field of explicit and numerical solutions of systems of PDEs of physics (nonlinear elasticity, elastoplasticity, hydrodynamics, multifluid flows, acoustics). The prerequisites are kept to introductory calculus level so that the book remains accessible at the same time to pure mathematicians (as a smoothand somewhat heuristic introdcution to this theory) and to applied mathematicians, numerical engineers and theoretical physicists (as a tool to treat problems involving products of distributions).
Book Synopsis Distributions and Their Applications in Physics by : F. Constantinescu
Download or read book Distributions and Their Applications in Physics written by F. Constantinescu and published by Elsevier. This book was released on 2017-07-26 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributions and Their Applications in Physics is the introduction of the Theory of Distributions and their applications in physics. The book contains a discussion of those topics under the Theory of Distributions that are already considered classic, which include local distributions; distributions with compact support; tempered distributions; the distribution theory in relativistic physics; and many others. The book also covers the Normed and Countably-normed Spaces; Test Function Spaces; Distribution Spaces; and the properties and operations involved in distributions. The text is recommended for physicists that wish to be acquainted with distributions and their relevance and applications as part of mathematical and theoretical physics, and for mathematicians who wish to be acquainted with the application of distributions theory for physics.
Book Synopsis Extreme Value Distributions by : Samuel Kotz
Download or read book Extreme Value Distributions written by Samuel Kotz and published by World Scientific. This book was released on 2000 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book provides an up-to-date comprehensive and down-to-earth survey of the theory and practice of extreme value distributions OCo one of the most prominent success stories of modern applied probability and statistics. Originated by E J Gumbel in the early forties as a tool for predicting floods, extreme value distributions evolved during the last 50 years into a coherent theory with applications in practically all fields of human endeavor where maximal or minimal values (the so-called extremes) are of relevance. The book is of usefulness both for a beginner with a limited probabilistic background and to expert in the field. Sample Chapter(s). Chapter 1.1: Historical Survey (139 KB). Chapter 1.2: The Three Types of Extreme Value Distributions (146 KB). Chapter 1.3: Limiting Distributions and Domain of Attraction (210 KB). Chapter 1.4: Distribution Function and Moments of Type 1 Distribution (160 KB). Chapter 1.5: Order Statistics, Record Values and Characterizations (175 KB). Contents: Univariate Extreme Value Distributions; Generalized Extreme Value Distributions; Multivariate Extreme Value Distributions. Readership: Applied probabilists, applied statisticians, environmental scientists, climatologists, industrial engineers and management experts."
Book Synopsis Distributions, Partial Differential Equations, and Harmonic Analysis by : Dorina Mitrea
Download or read book Distributions, Partial Differential Equations, and Harmonic Analysis written by Dorina Mitrea and published by Springer Science & Business Media. This book was released on 2013-09-20 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of distributions constitutes an essential tool in the study of partial differential equations. This textbook would offer, in a concise, largely self-contained form, a rapid introduction to the theory of distributions and its applications to partial differential equations, including computing fundamental solutions for the most basic differential operators: the Laplace, heat, wave, Lam\'e and Schrodinger operators.
Book Synopsis Elements of Distribution Theory by : Thomas A. Severini
Download or read book Elements of Distribution Theory written by Thomas A. Severini and published by Cambridge University Press. This book was released on 2005-08-08 with total page 3 pages. Available in PDF, EPUB and Kindle. Book excerpt: This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.
Book Synopsis Problems in Distributions and Partial Differential Equations by : C. Zuily
Download or read book Problems in Distributions and Partial Differential Equations written by C. Zuily and published by Elsevier. This book was released on 1988-04-01 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide a comprehensive introduction to the theory of distributions, by the use of solved problems. Although written for mathematicians, it can also be used by a wider audience, including engineers and physicists.The first six chapters deal with the classical theory, with special emphasis on the concrete aspects. The reader will find many examples of distributions and learn how to work with them. At the beginning of each chapter the relevant theoretical material is briefly recalled. The last chapter is a short introduction to a very wide and important field in analysis which can be considered as the most natural application of distributions, namely the theory of partial differential equations. It includes exercises on the classical differential operators and on fundamental solutions, hypoellipticity, analytic hypoellipticity, Sobolev spaces, local solvability, the Cauchy problem, etc.
Book Synopsis A Primer on Statistical Distributions by : Narayanaswamy Balakrishnan
Download or read book A Primer on Statistical Distributions written by Narayanaswamy Balakrishnan and published by John Wiley & Sons. This book was released on 2004-12-04 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed as an introduction to statistical distribution theory. * Includes a first chapter on basic notations and definitions that are essential to working with distributions. * Remaining chapters are divided into three parts: Discrete Distributions, Continuous Distributions, and Multivariate Distributions. * Exercises are incorporated throughout the text in order to enhance understanding of materials just taught.
