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A Guide to Distribution Theory and Fourier Transforms (Studies in Advanced Mathematics) [Hardcover]

Robert Strichartz (Editor)

5.0 out of 5 stars See all reviews (1 customer review) |

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Book Description

ISBN-10: 0849382734 | ISBN-13: 978-0849382734 | Publication Date: February 1, 1994 | Edition: 1

This book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudo-differential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.
in applied analysis and mathematical physics.

#outer_postBodyPS { display: none; } #psGradient { display: none; } #psPlaceHolder { display: none; } #psExpand { display: none; } This book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudo-differential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.
in applied analysis and mathematical physics.

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Editorial Reviews

Review

Strichartzs blend of generalized functions, Fourier analysis, and partial differential equations is unique. It [is] precisely this integrated basic triad that is most valuable, and one can argue, should be presented to all undergraduates majoring in mathematics. It is beautiful, elegant mathematics, and it is quite useful as well.
John A. Synowiec, in American Mathematical Monthly
Strichartzs blend of generalized functions, Fourier analysis, and partial differential equations is unique. It [is] precisely this integrated basic triad that is most valuable, and one can argue, should be presented to all undergraduates majoring in mathematics. It is beautiful, elegant mathematics, and it is quite useful as well.
John A. Synowiec, in American Mathematical Monthly

From the Publisher

Readership: Graduate students and researchers in pure or applied mathematics and related disciplines. --This text refers to an alternate Hardcover edition.

Product Details

Hardcover: 224 pages
Publisher: CRC-Press; 1 edition (February 1, 1994)
Language: English
ISBN-10: 0849382734
ISBN-13: 978-0849382734
Product Dimensions: 9.8 x 6.5 x 0.8 inches
Shipping Weight: 1 pounds

Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)

Amazon Best Sellers Rank: #2,006,697 in Books (See Top 100 in Books)

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10 of 10 people found the following review helpful:

5.0 out of 5 stars Excellent, September 17, 2007

TOE (Paris, France) - See all my reviews

This review is from: Guide to Distribution Theory and Fourier (Hardcover)

Distributions are objects most physicists will frequently encounter during their career, but, surprinsingly, the subject is not given the place it deserves in the current ordinary science curriculum.
I would particularly recommend this book to physics students willing to learn the foundation of distribution theory and its close ties to Fourier transforms. Distribution theory is, basically speaking, a way of making rigorous the operations physicists find Ok to carry on functions, that otherwise wouldn't rigorously make sense. Distribution theory therefore provides a useful way of checking, in the process of a calculation, if it is allowed (according to the extended rules of distribution theory), or if it is definitely dubious (e.g. current distribution theory doesn't provide a mean of making sense of a product of Dirac delta functions, while such expressions sometimes pop out in the context of quantum field theory ; nevertheless, there exist other formal theories, such as Colombo calculus that aim at justifying this ; yet, for some reason, they seem to bear less power than the original distribution theory).
This work is an easy, gentle, pedagogical piece of mathematical exposition.
The subject is wonderfully motivated.
As such, this book is suited to self-study.
It could also be used as a textbook for an introductory course on the subject, or as an introductory reading to more advanced texts (Aizenman, for instance).
Highly recommended.

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Inside This Book (learn more)
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First Sentence:
You have often been asked to consider a function f (x) as representing the value of a physical variable at a particular point x in space (or space-time). Read the first page

Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
wave front set, adjoint identity, bicharacteristic curves, scaling identity, adjoint identities, transform side, positive distribution, singular support, tempered distribution, approximate identity, compact support, coefficient operators, wave operator, classical symbol, test functions, pseudodifferential operators

Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Structure of Distributions, Use the Plancherel

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Citations (learn more)

This book cites 1 book:

Ten Lectures on Wavelets (CBMS-NSF Regional Conference Series in Applied Mathematics) by Ingrid Daubechies in Back Matter

33 books cite this book:

Applied Mathematics by J. David Logan on page 238, and page 289
Stereology and Stochastic Geometry (Computational Imaging and Vision) by John E. Hilliard on page 68
Generalized Functions: Theory and Technique by Ram P. Kanwal in Back Matter
Geometric Tomography (Encyclopedia of Mathematics and its Applications) by Richard J. Gardner in Back Matter
Real Analysis: An Introduction to the Theory of Real Functions and Integration by Jewgeni H. Dshalalow in Front Matter

See all 33 books citing this book

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