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ISBN 10: 0817640061 ISBN 13: 9780817640064

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**Item Description: **BirkhÃƒÂ¤user Boston. Paperback. Book Condition: New. This item is printed on demand. Paperback. 496 pages. 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 This item ships from La Vergne,TN. Paperback. Bookseller Inventory # 9780817643430

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Published by Academic Press (1983)

ISBN 10: 0124110185 ISBN 13: 9780124110182

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**Item Description: **BirkhÃ¤user. Paperback. Book Condition: New. Paperback. 474 pages. Dimensions: 9.7in. x 7.0in. x 1.1in.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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Bookseller Inventory # 9781468400373

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Published by Birkhauser (1993)

ISBN 10: 0817637168 ISBN 13: 9780817637163

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**Item Description: **Book Condition: New. Publisher/Verlag: Springer, Berlin | Theory and Technique | 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. | 1. The Dirac Delta Function and Delta Sequences.- 1.1. The heaviside function.- 1.2. The Dirac delta function.- 1.3. The delta sequences.- 1.4. A unit dipole.- 1.5. The heaviside sequences.- Exercises.- 2. The Schwartz-Sobolev Theory of distributions.- 2.1. Some introductory definitions.- 2.2. Test functions.- 2.3. Linear functionals and the Schwartz-Sobolev theory of distributions.- 2.4. Examples.- 2.5. Algebraic operations on distributions.- 2.6. Analytic operations on distributions.- 2.7. Examples.- 2.8. The support and singular support of a distribution.- Exercises.- 3. Additional Properties of Distributions.- 3.1. Transformation properties of the delta distribution.- 3.2. Convergence of distributions.- 3.3. Delta sequences with parametric dependence.- 3.4. Fourier series.- 3.5. Examples.- 3.6. The delta function as a Stieltjes integral.- Exercises.- 4. Distributions Defined by Divergent Integrals.- 4.1. Introduction.- 4.2. The pseudofunction H(x)/xn, n = 1, 2, 3,.- 4.3. Functions with algebraic singularity of order m.- 4.4. Examples.- Exercises.- 5. Distributional Derivatives of Functions with Jump Discontinuities.- 5.1. Distributional derivatives in R1.- 5.2. Moving surfaces of discontinuity in Rn, n ? 2.- 5.3. Surface distributions.- 5.4. Various other representations.- 5.5. First-order distributional derivatives.- 5.6. Second-order distributional derivatives.- 5.7. Higher-order distributional derivatives.- 5.8. The two-dimensional case.- 5.9. Examples.- 5.10. The function Pf(1/r) and its derivatives.- 6. Tempered Distributions and the Fourier Transform.- 6.1. Preliminary concepts.- 6.2. Distributions of slow growth (tempered distributions).- 6.3. The Fourier transform.- 6.4. Examples.- Exercises.- 7. Direct Products and Convolutions of Distributions.- 7.1. Definition of the direct product.- 7.2. The direct product of tempered distributions.- 7.3. The Fourier transform of the direct product of tempered distributions.- 7.4. The convolution.- 7.5. The role of convolution in the regularization of the distributions.- 7.6. The dual spaces E and E?.- 7.7. Examples.- 7.8. The Fourier transform of a convolution.- 7.9. Distributional solutions of integral equations.- Exercises.- 8. The Laplace Transform.- 8.1. A brief discussion of the classical results.- 8.2. The Laplace transform distributions.- 8.3. The Laplace transform of the distributional derivatives and vice versa. Bookseller Inventory # K9781468400373

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Published by Springer-Verlag New York Inc., United States (2012)

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**Item Description: **Springer-Verlag New York Inc., United States, 2012. Paperback. Book Condition: New. 2nd ed. 1998. 246 x 178 mm. Language: English . Brand New Book. 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. Bookseller Inventory # KNV9781468400373

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Published by Birkh? (2012)

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Published by Birkhäuser Boston (1999)

ISBN 10: 0817640851 ISBN 13: 9780817640859

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Published by Birkhäuser (2012)

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Published by BirkhÃ¤user Boston 2004-07-23 (2004)

ISBN 10: 0817643435 ISBN 13: 9780817643430

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Published by BIRKHAUSER BOSTON INC, United States (2002)

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**Item Description: **BIRKHAUSER BOSTON INC, United States, 2002. Hardback. Book Condition: New. 2nd ed. 2002. 236 x 157 mm. Language: English . Brand New Book ***** Print on Demand *****. .The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book.[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is. - The Bulletin of Mathematics Books (Review of the 1st edition) ** .The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field.most of the material has appeared in no other book. - SIAM News (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic. Bookseller Inventory # APC9780817641429

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Published by Birkhäuser (2012)

ISBN 10: 1461271231 ISBN 13: 9781461271239

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Published by Birkhäuser Jan 2012 (2012)

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**Item Description: **Birkhäuser Jan 2012, 2012. Taschenbuch. Book Condition: Neu. 254x178x25 mm. Neuware - 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. 476 pp. Englisch. Bookseller Inventory # 9781468400373

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