Generalized Functions And Fourier Analysis
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Generalized Functions and Fourier Analysis
Author | : Michael Oberguggenberger,Joachim Toft,Jasson Vindas,Patrik Wahlberg |
Publsiher | : Birkhäuser |
Total Pages | : 276 |
Release | : 2017-05-06 |
Genre | : Mathematics |
ISBN | : 9783319519111 |
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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.
An Introduction to Fourier Analysis and Generalised Functions
Author | : Sir M. J. Lighthill |
Publsiher | : Cambridge University Press |
Total Pages | : 112 |
Release | : 1958 |
Genre | : Mathematics |
ISBN | : 0521091284 |
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"Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof...." Science Progress
Introduction to Fourier Analysis and Generalised Functions
Author | : Sir M J Lighthill |
Publsiher | : Hassell Street Press |
Total Pages | : 92 |
Release | : 2021-09-09 |
Genre | : Electronic Book |
ISBN | : 1013715624 |
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This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Generalized Functions and Fourier Analysis
Author | : John L. Challifour |
Publsiher | : Unknown |
Total Pages | : 208 |
Release | : 1972 |
Genre | : Mathematics |
ISBN | : UOM:39015015691564 |
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Applications of Fourier Transforms to Generalized Functions
Author | : M. Rahman |
Publsiher | : WIT Press |
Total Pages | : 193 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 9781845645649 |
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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
Introduction to Fourier Analysis and Generalised Functions
Author | : Sir M. J. Lighthill |
Publsiher | : Unknown |
Total Pages | : 96 |
Release | : 1964 |
Genre | : Fourier analysis |
ISBN | : MINN:31951002106956X |
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Generalized Functions Theory and Technique
Author | : Ram P. Kanwal |
Publsiher | : Springer Science & Business Media |
Total Pages | : 474 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9781468400359 |
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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.
A First Course in Fourier Analysis
Author | : David W. Kammler |
Publsiher | : Cambridge University Press |
Total Pages | : 39 |
Release | : 2008-01-17 |
Genre | : Mathematics |
ISBN | : 9781139469036 |
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This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.