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Generalised Functions
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Book Synopsis Generalized Functions Theory and Technique by : Ram P. Kanwal
Download or read book Generalized Functions Theory and Technique written by Ram P. Kanwal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition of Generalized Functions has been strengthened in many ways. The already extensive set of examples has been expanded. Since the publication of the first edition, there has been tremendous growth in the subject and I have attempted to incorporate some of these new concepts. Accordingly, almost all the chapters have been revised. The bibliography has been enlarged considerably. Some of the material has been reorganized. For example, Chapters 12 and 13 of the first edition have been consolidated into Chapter 12 of this edition by a judicious process of elimination and addition of the subject matter. The new Chapter 13 explains the interplay between the theories of moments, asymptotics, and singular perturbations. Similarly, some sections of Chapter 15 have been revised and included in earlier chapters to improve the logical flow of ideas. However, two sections are retained. The section dealing with the application of the probability theory has been revised, and I am thankful to Professor Z.L. Crvenkovic for her help. The new material included in this chapter pertains to the modern topics of periodic distributions and microlocal theory. I have demonstrated through various examples that familiarity with the generalized functions is very helpful for students in physical sciences and technology. For instance, the reader will realize from Chapter 6 how the generalized functions have revolutionized the Fourier analysis which is being used extensively in many fields of scientific activity.
Book Synopsis The Theory of Generalised Functions by : D. S. Jones
Download or read book The Theory of Generalised Functions written by D. S. Jones and published by Cambridge University Press. This book was released on 2009-01-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from an elementary level Professor Jones discusses generalised functions and their applications. He aims to supply the simplest introduction for those who wish to learn to use generalised functions and there is liberal provision of exercises with which to gain experience. The study of more advanced topics such as partial differential equations, Laplace transforms and ultra-distributions should also make it a valuable source for researchers. The demands placed upon the reader's analytical background are the minimum required to approach this topic. Therefore, by selecting chapters it is possible to construct a short introductory course for students, a final-year option for honours undergraduates or a comprehensive postgraduate course.
Book Synopsis Geometric Theory of Generalized Functions with Applications to General Relativity by : M. Grosser
Download or read book Geometric Theory of Generalized Functions with Applications to General Relativity written by M. Grosser and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in in ternal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these develop ments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of sub ordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent mono graphs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our intro duction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transpar ent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter.
Book Synopsis Methods of the Theory of Generalized Functions by : V. S. Vladimirov
Download or read book Methods of the Theory of Generalized Functions written by V. S. Vladimirov and published by CRC Press. This book was released on 2002-08-15 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems, and boundary values of helomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogenous generalized functions, and multiplication of generalized functions. This book will meet the needs of researchers, engineers, and students of applied mathematics, control theory, and the engineering sciences.
Book Synopsis Generalized Functions, Volume 1 by : I. M. Gel′fand
Download or read book Generalized Functions, Volume 1 written by I. M. Gel′fand and published by American Mathematical Soc.. This book was released on 2016-04-19 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: he first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel′fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. Volume 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables.
Book Synopsis An Introduction to Fourier Analysis and Generalised Functions by : M. J. Lighthill
Download or read book An Introduction to Fourier Analysis and Generalised Functions written by M. J. Lighthill and published by . This book was released on 1958 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof...." Science Progress
Book Synopsis Generalized Functions and Fourier Analysis by : Michael Oberguggenberger
Download or read book Generalized Functions and Fourier Analysis written by Michael Oberguggenberger and published by Birkhäuser. This book was released on 2017-05-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.
Book Synopsis An Introduction to Fourier Analysis and Generalised Functions by : Sir M. J. Lighthill
Download or read book An Introduction to Fourier Analysis and Generalised Functions written by Sir M. J. Lighthill and published by Cambridge University Press. This book was released on 1958 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof...." Science Progress
Book Synopsis Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics by : W.-H. Steeb
Download or read book Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics written by W.-H. Steeb and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics. Audience: The book is suitable for graduate students in physics and mathematics.
Book Synopsis Eigenvalues, Embeddings and Generalised Trigonometric Functions by : Jan Lang
Download or read book Eigenvalues, Embeddings and Generalised Trigonometric Functions written by Jan Lang and published by Springer Science & Business Media. This book was released on 2011-03-23 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of the book is the study, from the standpoint of s-numbers, of integral operators of Hardy type and related Sobolev embeddings. In the theory of s-numbers the idea is to attach to every bounded linear map between Banach spaces a monotone decreasing sequence of non-negative numbers with a view to the classification of operators according to the way in which these numbers approach a limit: approximation numbers provide an especially important example of such numbers. The asymptotic behavior of the s-numbers of Hardy operators acting between Lebesgue spaces is determined here in a wide variety of cases. The proof methods involve the geometry of Banach spaces and generalized trigonometric functions; there are connections with the theory of the p-Laplacian.
Book Synopsis Theories of Generalised Functions by : R F Hoskins
Download or read book Theories of Generalised Functions written by R F Hoskins and published by Elsevier. This book was released on 2005-01-01 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explaining and comparing the various standard types of generalised functions which have been developed during the 20th Century, this text also contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions. The book could readily be used as a main text on generalised functions for mathematical undergraduates in final year analysis courses, as it presupposes little more than a general mathematical background. It also makes a valuable reference text for non-specific applied mathematics students, such as physicists or electrical engineers, needing to gain expertise in the application of generalised functions to physical problems, without any prior acquaintance of the specialised subject matter. An ideal companion book to Delta Functions, also by Professor Hoskins. Explains and compares the various standard types of generalised functions that have been developed during the 20th Century Contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions
Download or read book Delta Functions written by R F Hoskins and published by Elsevier. This book was released on 2009-03-31 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delta Functions has now been updated, restructured and modernised into a second edition, to answer specific difficulties typically found by students encountering delta functions for the first time. In particular, the treatment of the Laplace transform has been revised with this in mind. The chapter on Schwartz distributions has been considerably extended and the book is supplemented by a fuller review of Nonstandard Analysis and a survey of alternative infinitesimal treatments of generalised functions. Dealing with a difficult subject in a simple and straightforward way, the text is readily accessible to a broad audience of scientists, mathematicians and engineers. It can be used as a working manual in its own right, and serves as a preparation for the study of more advanced treatises. Little more than a standard background in calculus is assumed, and attention is focused on techniques, with a liberal selection of worked examples and exercises. Second edition has been updated, restructured and modernised to answer specific difficulties typically found by students encountering delta functions for the first time Attention is focused on techniques, with a liberal selection of worked examples and exercises Readily accessible to a broad audience of scientists, mathematicians and engineers and can be used as a working manual in its own right
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 Generalized Functions, Volume 2 by : I. M. Gel'fand
Download or read book Generalized Functions, Volume 2 written by I. M. Gel'fand and published by American Mathematical Soc.. This book was released on 2016-03-30 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel'fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. Volume 2 is devoted to detailed study of generalized functions as linear functionals on appropriate spaces of smooth test functions. In Chapter 1, the authors introduce and study countable-normed linear topological spaces, laying out a general theoretical foundation for the analysis of spaces of generalized functions. The two most important classes of spaces of test functions are spaces of compactly supported functions and Schwartz spaces of rapidly decreasing functions. In Chapters 2 and 3 of the book, the authors transfer many results presented in Volume 1 to generalized functions corresponding to these more general spaces. Finally, Chapter 4 is devoted to the study of the Fourier transform; in particular, it includes appropriate versions of the Paley-Wiener theorem.
Book Synopsis Integral Transforms of Generalized Functions and Their Applications by : Ram Shankar Pathak
Download or read book Integral Transforms of Generalized Functions and Their Applications written by Ram Shankar Pathak and published by Routledge. This book was released on 2017-07-05 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: For those who have a background in advanced calculus, elementary topology and functional analysis - from applied mathematicians and engineers to physicists - researchers and graduate students alike - this work provides a comprehensive analysis of the many important integral transforms and renders particular attention to all of the technical aspects of the subject. The author presents the last two decades of research and includes important results from other works.
Book Synopsis Generalized Hypergeometric Functions by : Lucy Joan Slater
Download or read book Generalized Hypergeometric Functions written by Lucy Joan Slater and published by . This book was released on 1993 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Generalised Thermostatistics by : Jan Naudts
Download or read book Generalised Thermostatistics written by Jan Naudts and published by Springer Science & Business Media. This book was released on 2011-02-07 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The domain of non-extensive thermostatistics has been subject to intensive research over the past twenty years and has matured significantly. Generalised Thermostatistics cuts through the traditionalism of many statistical physics texts by offering a fresh perspective and seeking to remove elements of doubt and confusion surrounding the area. The book is divided into two parts - the first covering topics from conventional statistical physics, whilst adopting the perspective that statistical physics is statistics applied to physics. The second developing the formalism of non-extensive thermostatistics, of which the central role is played by the notion of a deformed exponential family of probability distributions. Presented in a clear, consistent, and deductive manner, the book focuses on theory, part of which is developed by the author himself, but also provides a number of references towards application-based texts. Written by a leading contributor in the field, this book will provide a useful tool for learning about recent developments in generalized versions of statistical mechanics and thermodynamics, especially with respect to self-study. Written for researchers in theoretical physics, mathematics and statistical mechanics, as well as graduates of physics, mathematics or engineering. A prerequisite knowledge of elementary notions of statistical physics and a substantial mathematical background are required.
