Generalised Functions

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Generalized Functions Theory And Technique

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Author : Ram P. Kanwal
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-01-01

Generalized Functions Theory And Technique written by Ram P. Kanwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.

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.

Theories Of Generalised Functions

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Author : R F Hoskins
language : en
Publisher: Elsevier
Release Date : 2005-01-01

Theories Of Generalised Functions written by R F Hoskins and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.

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

An Introduction To Fourier Analysis And Generalised Functions

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Author : Sir M. J. Lighthill
language : en
Publisher: Cambridge University Press
Release Date : 1958

An Introduction To Fourier Analysis And Generalised Functions written by Sir M. J. Lighthill and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Mathematics categories.

"Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof...." Science Progress

Generalised Functions

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Author : R. F. Hoskins
language : en
Publisher:
Release Date : 1979

Generalised Functions written by R. F. Hoskins and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.

The long history of prejudice against women has been the focus of many academic studies, but until now there has been no attempt to collect actual examples of this prejudice from books, articles, and scholarly monographs. Now S.T. Joshi has gathered together dozens of works that document the scorn and contempt for the weaker sex that most women endured for countless generations until very recently. As Joshi points out, this is the work, not of a few isolated cranks, but of the leading members of the intellectual, social, and political communities: scientists, educators, clerics, and politicians. Reading the unabashed bias against women so evident in these pages brings the entrenched misogyny of American society into vivid focus and makes one appreciate all the more the immense efforts of feminists who for more than a century have worked to overcome the stereotypes of womanly behavior long enforced by men.

Generalized Functions And Their Applications

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Author : R.S. Pathak
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Generalized Functions And Their Applications written by R.S. Pathak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Social Science categories.

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.

Hilbert Spaces Wavelets Generalised Functions And Modern Quantum Mechanics

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Author : W.-H. Steeb
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07

Hilbert Spaces Wavelets Generalised Functions And Modern Quantum Mechanics written by W.-H. Steeb and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Science categories.

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.

Generalised Functions

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Author : Douglas Samuel Jones
language : en
Publisher:
Release Date : 1966

Generalised Functions written by Douglas Samuel Jones and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Theory of distributions (Functional analysis). categories.

Nonlinear Theory Of Generalized Functions

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Author : Michael Oberguggenberger
language : en
Publisher: CRC Press
Release Date : 1999-03-16

Nonlinear Theory Of Generalized Functions written by Michael Oberguggenberger and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-16 with Mathematics categories.

Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities. A workshop held at the Erwin-Schrödinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and general relativity, stochastic partial differential equations, and nonstandard analysis. The authors provide the latest research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models. The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical methods.

Delta Functions

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Author : R F Hoskins
language : en
Publisher: Elsevier
Release Date : 2009-03-31

Delta Functions written by R F Hoskins and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-31 with Mathematics categories.

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

Generalized Functions

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Author : Ram P. Kanwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Generalized Functions written by Ram P. Kanwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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 hasbeen tremendous growth inthe subject and Ihave 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 12ofthis edition by ajudicious 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 to 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 modem 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.