Generalized Functions And Their Applications

Author : Ram P. Kanwal
Publisher : Springer Science & Business Media
Page : 474 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468400359

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Generalized Functions Theory and Technique by Ram P. Kanwal Pdf

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.

Author : Ram Shankar Pathak
Publisher : Routledge
Page : 432 pages
File Size : 44,9 Mb
Release : 2017-07-05
Category : History
ISBN : 9781351562690

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Integral Transforms of Generalized Functions and Their Applications by Ram Shankar Pathak Pdf

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.

Author : R.S. Pathak
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 50,7 Mb
Release : 2013-11-11
Category : Social Science
ISBN : 9781489915917

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Generalized Functions and Their Applications by R.S. Pathak Pdf

The International Symposium on Generalized Functions and Their Applications was organized by the Department of Mathematics, Banaras Hindu University, and held December 23-26, 1991, on the occasion of the Platinum Jubilee Celebration of the university. More than a hundred mathematicians from ten countries participated in the deliberations of the symposium. Thirty lectures were delivered on a variety of topics within the area. The contributions to the proceedings of the symposium are, with a few exceptions, expanded versions of the lectures delivered by the invited speakers. The survey papers by Komatsu and Hoskins and Sousa Pinto provide an up-to-date account of the theory of hyperfunctions, ultradistributions and microfunctions, and the nonstandard theory of new generalized functions, respectively; those by Stankovic and Kanwal deal with structures and asymptotics. Choquet-Bruhat's work studies generalized functions on manifold and gives applications to shocks and discrete models. The other contributions relate to contemporary problems and achievements in theory and applications, especially in the theory of partial differential equations, differential geometry, mechanics, mathematical physics, and systems science. The proceedings give a very clear impression of the present state of the art in this field and contain many challenges, ideas, and open problems. The volume is very helpful for a broad spectrum of readers: graduate students to mathematical researchers.

Author : Michael Grosser
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 51,8 Mb
Release : 2001-11-30
Category : Mathematics
ISBN : 1402001452

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Geometric Theory of Generalized Functions with Applications to General Relativity by Michael Grosser Pdf

This work provides the first comprehensive introduction to the nonlinear theory of generalized functions (in the sense of Colombeau's construction) on differentiable manifolds. Particular emphasis is laid on a diffeomorphism invariant geometric approach to embedding the space of Schwartz distributions into algebras of generalized functions. The foundations of a `nonlinear distributional geometry' are developed, supplying a solid base for an increasing number of applications of algebras of generalized functions to questions of a primarily geometric mature, in particular in mathematical physics. Applications of the resulting theory to symmetry group analysis of differential equations and the theory of general relativity are presented in separate chapters. These features distinguish the present volume from earlier introductory texts and monographs on the subject. Audience: The book will be of interest to graduate students as well as to researchers in functional analysis, partial differential equations, differential geometry, and mathematical physics.

Author : Ram P. Kanwal
Publisher : Springer Science & Business Media
Page : 490 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681746

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Generalized Functions by Ram P. Kanwal Pdf

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 : M. Rahman
Publisher : WIT Press
Page : 193 pages
File Size : 54,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9781845645649

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Applications of Fourier Transforms to Generalized Functions by M. Rahman Pdf

The generalized function is one of the important branches of mathematics which has enormous applications in practical fields. In particular its applications to the theory of distribution and signal processing are very much essential. In this computer age, information science plays a very important role and the Fourier transform is extremely significant in deciphering obscured information to be made understandable. The book contains six chapters and three appendices. Chapter 1 deals with the preliminary remarks of Fourier series from general point of view. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. Chapter 4 deals with the asymptotic estimation of Fourier transforms. Chapter 5 is devoted to the study of Fourier series as a series of generalized functions. Chapter 6 deals with the fast Fourier transforms.Appendix A contains the extended list of Fourier transform pairs.Appendix B illustrates the properties of impulse function.Appendix C contains an extended list of biographical references

Author : F. Farassat
Publisher : Unknown
Page : 60 pages
File Size : 52,6 Mb
Release : 1994
Category : Aerodynamics
ISBN : NASA:31769000447469

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Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics by F. Farassat Pdf

Author : V. S. Vladimirov
Publisher : CRC Press
Page : 332 pages
File Size : 46,6 Mb
Release : 2002-08-15
Category : Mathematics
ISBN : 0415273560

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Methods of the Theory of Generalized Functions by V. S. Vladimirov Pdf

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.

Author : I. M. Gel′fand,G. E. Shilov
Publisher : American Mathematical Soc.
Page : 423 pages
File Size : 48,6 Mb
Release : 2016-04-19
Category : Theory of distributions (Functional analysis)
ISBN : 9781470426583

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Generalized Functions, Volume 1 by I. M. Gel′fand,G. E. Shilov Pdf

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.

Author : Michael Oberguggenberger,Joachim Toft,Jasson Vindas,Patrik Wahlberg
Publisher : Birkhäuser
Page : 276 pages
File Size : 54,6 Mb
Release : 2017-05-06
Category : Mathematics
ISBN : 9783319519111

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Generalized Functions and Fourier Analysis by Michael Oberguggenberger,Joachim Toft,Jasson Vindas,Patrik Wahlberg Pdf

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.

Author : V.S. Vladimirov,Yu.N. Drozzinov,O.I. Zavialov
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400928312

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Tauberian Theorems for Generalized Functions by V.S. Vladimirov,Yu.N. Drozzinov,O.I. Zavialov Pdf

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. The Scandal of Father G. K. Chesterton. 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Author : Bogoljub Stankovic
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461310556

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Generalized Functions, Convergence Structures, and Their Applications by Bogoljub Stankovic Pdf

This Proceedings consists of a collection of papers presented at the International Conference "Generalized functions, convergence structures and their applications" held from June 23-27, 1987 in Dubrovnik, Yugoslavia (GFCA-87): 71 participants from 21 countr~es from allover the world took part in the Conference. Proceedings reflects the work of the Conference. Plenary lectures of J. Burzyk, J. F. Colombeau, W. Gahler, H. Keiter, H. Komatsu, B. Stankovic, H. G. Tillman, V. S. Vladimirov provide an up-to-date account of the cur rent state of the subject. All these lectures, except H. G. Tillman's, are published in this volume. The published communications give the contemporary problems and achievements in the theory of generalized functions, in the theory of convergence structures and in their applications, specially in the theory of partial differential equations and in the mathematical physics. New approaches to the theory of generalized functions are presented, moti vated by concrete problems of applications. The presence of articles of experts in mathematical physics contributed to this aim. At the end of the volume one can find presented open problems which also point to further course of development in the theory of generalized functions and convergence structures. We are very grateful to Mr. Milan Manojlovic who typed these Proce edings with extreme skill and diligence and with inexhaustible patience.

Author : R.S. Pathak
Publisher : Unknown
Page : 128 pages
File Size : 42,8 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 2884492186

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Integral Transforms of Generalized Functions and Their Application by R.S. Pathak Pdf

Author : A.H. Zemanian
Publisher : Courier Corporation
Page : 400 pages
File Size : 43,7 Mb
Release : 2011-11-30
Category : Mathematics
ISBN : 9780486151946

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Distribution Theory and Transform Analysis by A.H. Zemanian Pdf

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.

Author : Vasiliĭ Sergeevich Vladimirov
Publisher : Unknown
Page : 384 pages
File Size : 46,5 Mb
Release : 1979
Category : Functions
ISBN : UCAL:B3435818

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Generalized Functions in Mathematical Physics by Vasiliĭ Sergeevich Vladimirov Pdf