Resources for theory of distributions (generalized functions) for physicists

Question

I am looking for tutorials, articles or books containing theory of distributions in context of mathematical physics. Please suggest.

This post imported from StackExchange Physics at 2015-10-02 08:00 (UTC), posted by SE-user user41451

Comments

Related: mathoverflow.net/q/20314/13917 and math.stackexchange.com/q/13711/11127 Related: physics.stackexchange.com/q/125917/2451

This post imported from StackExchange Physics at 2015-10-02 08:00 (UTC), posted by SE-user Qmechanic

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One of the appendices to Mukhanov's recent textbook on quantum effects in gravity gives a nice intro to the theory of distributions: I found it very enlightening

This post imported from StackExchange Physics at 2015-10-02 08:00 (UTC), posted by SE-user Danu

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@Danu I found it informative.

This post imported from StackExchange Physics at 2015-10-02 08:00 (UTC), posted by SE-user user41451

Answer 1

In addition to the books already listed there is the nice (excellent in my opinion) textbook by Friedlander and Joshi, Introduction to the theory of Distributions

This post imported from StackExchange Physics at 2015-10-02 08:01 (UTC), posted by SE-user Valter Moretti

Comments

Googling for author and title, I found the following lecture notes from Princeton, https://web.math.princeton.edu/~seri/homepage/courses/Analysis2008.pdf, "Lecture Notes 2008" by Sergiu Klainerman, because it cites Friedlander and Joshi on its first page. As well as the Klainerman having what looks a worthwhile 25 pages on distributions, it also suggests "Hormander's first volume of The Analysis of Linear Partial Differential Operators, [5], in Springer can also be useful."

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In my view, Hoermander's first volume of The Analysis of Linear Partial Differential Operators is useful for a bit advanced readers. Sometimes there are statements which are  obvious just to Hoermander himself...(Especially in the section regarding microlocal analysis). I use those books, but I would not suggest them as intial references.

Answer 2

I found following books useful:

1. A Guide to Distribution Theory and Fourier Transforms By Robert S. Strichartz. Not very rigorous and not much content either. But good book to start from.
2. Generalized Functions: Theory and Applications By Ram P. Kanwal. Not very rigorous. This book starts with chapter on Dirac delta function and then slowly builds the theory. There are many chapters on applications in Physics and Engineering.
3. Equations of Mathematical Physics by V. S. Vladimirov. Rigorous and Pedantic.

This post imported from StackExchange Physics at 2015-10-02 08:01 (UTC), posted by SE-user user41451