A Guide to Distribution Theory and Fourier Transforms
eBook - PDF

A Guide to Distribution Theory and Fourier Transforms

  1. 236 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

A Guide to Distribution Theory and Fourier Transforms

About this book

This important 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 pseudodifferential 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.

A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.

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Yes, you can access A Guide to Distribution Theory and Fourier Transforms by Robert S Strichartz in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.

Information

Publisher
WSPC
Year
2003
eBook ISBN
9789813102293
Topic
Mathematics
Subtopic
Applied Mathematics
Index
Mathematics
6 
1 
What 
are 
Distributions? 
2-
f%f
k
(x)dx
=
l. 
The 
simplest 
examples 
are 
or 
Figure 
1.2 
but 
we 
may 
want 
to 
take
fk
smoother, 
even 
in
T> 
Figure 
1.3 
Now 
the 
distribution 
(fk,V>) 
=
/
fk(x)ip{x)dx 
is 
an 
average 
of
<p
near 
zero, 
so 
that 
if
<p
does 
not 
vary 
much 
in 
—1/fc 
< 
x 
<
1/fc, 
it 
is 
close 
to
<p(0).
Certainly 
in 
the 
limit 
as 
fc 
—> 
oo 
we 
get 

Table of contents

  1. Contents
  2. Preface
  3. 1 What are Distributions?
  4. 2 The Calculus of Distributions
  5. 3 Fourier Transforms
  6. 4 Fourier Transforms of Tempered Distributions
  7. 5 Solving Partial Differential Equations
  8. 6 The Structure of Distributions
  9. 7 Fourier Analysis
  10. 8 Sobolev Theory and Microlocal Analysis
  11. Suggestions for Further Reading
  12. Index