Distributions: Theory and Applications (Cornerstones)

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9780817646721: Distributions: Theory and Applications (Cornerstones)

This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.

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From the Back Cover:

This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. Throughout the book, methods are developed to deal with formal calculations involving functions, series, and integrals that cannot be mathematically justified within the classical framework.

Key features:

· Many examples, exercises, hints, and solutions guide the reader throughout the text.

· Includes an introduction to distributions, differentiation, convergence, convolution, the Fourier transform, and spaces of distributions having special properties.

· Original proofs, which may be difficult to locate elsewhere, are given for many well-known results.

· The Fourier transform is transparently treated and applied to provide a new proof of the Kernel Theorem, which in turn is used to efficiently derive numerous important results.

· The systematic use of pullback and pushforward introduces concise notation.

· Emphasizes the role of symmetry in obtaining short arguments and investigates distributions that are invariant under the actions of various groups of transformations.

Distributions: Theory and Applications is aimed at advanced undergraduates and graduate students in mathematics, theoretical physics, and engineering, who will find this textbook a welcome introduction to the subject, requiring only a minimal mathematical background. The work may also serve as an excellent self-study guide for researchers who use distributions in various fields.

About the Author:

Hans Duistermaat was a geometric analyst, who unexpectedly passed away in March 2010. His research encompassed many different areas in mathematics: ordinary differential equations, classical mechanics, discrete integrable systems, Fourier integral operators and their application to partial differential equations and spectral problems, singularities of mappings, harmonic analysis on semisimple Lie groups, symplectic differential geometry, and algebraic geometry. He was (co-)author of eleven books.

Duistermaat was affiliated with the Mathematical Institute of Utrecht University since 1974 as a Professor of Pure and Applied Mathematics. During the last five years he was honored with a special professorship at Utrecht University endowed by the Royal Netherlands Academy of Arts and Sciences. He was also a member of the Academy since 1982. He had 23 PhD students.

Johan Kolk has published in the areas of harmonic analysis on semisimple Lie groups, the theory of distributions, and classical analysis. Jointly with Duistermaat, he has written four books: besides the present one, one on Lie groups, and another on multidimensional real analysis. Until his retirement in 2009, he was affiliated with the Mathematical Institute of Utrecht University. For more information, see http://www.staff.science.uu.nl/~kolk0101/

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J.J. Duistermaat; Johan A.C. Kolk
ISBN 10: 0817646728 ISBN 13: 9780817646721
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J. J. Duistermaat, J. A. C. Kolk
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Descrizione libro BIRKHAUSER BOSTON INC, United States, 2010. Hardback. Condizione libro: New. 2010. Language: English . Brand New Book. This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background. Codice libro della libreria AAU9780817646721

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J. J. Duistermaat, J. A. C. Kolk
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Descrizione libro BIRKHAUSER BOSTON INC, United States, 2010. Hardback. Condizione libro: New. 2010. Language: English . Brand New Book. This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background. Codice libro della libreria AAU9780817646721

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Descrizione libro Birkhäuser Boston 2010-08-17, New York |London, 2010. hardback. Condizione libro: New. Codice libro della libreria 9780817646721

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Descrizione libro Birkh?user, 2010. Condizione libro: New. 2010. 2010th Edition. Hardcover. This text offers an application-oriented introduction to the theory of distributions. It presents distributions as a natural method of analysis from a mathematical and physical point of view. The subject is motivated by many exercises, hints and solutions. Series: Cornerstones. Num Pages: 461 pages, 41 black & white illustrations, biography. BIC Classification: PBKF. Category: (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 234 x 156 x 25. Weight in Grams: 1820. . . . . . . Codice libro della libreria V9780817646721

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Descrizione libro Birkhauser Boston Inc. Hardback. Condizione libro: new. BRAND NEW, Distributions: Theory and Applications (2010), J. J. Duistermaat, J. A. C. Kolk, This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background. Codice libro della libreria B9780817646721

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J.J. Duistermaat; Johan A.C. Kolk
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Descrizione libro Birkhäuser. Condizione libro: New. 2010. 2010th Edition. Hardcover. This text offers an application-oriented introduction to the theory of distributions. It presents distributions as a natural method of analysis from a mathematical and physical point of view. The subject is motivated by many exercises, hints and solutions. Series: Cornerstones. Num Pages: 461 pages, 41 black & white illustrations, biography. BIC Classification: PBKF. Category: (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 234 x 156 x 25. Weight in Grams: 1820. . . . . . Books ship from the US and Ireland. Codice libro della libreria V9780817646721

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