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.

Answer 1

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.

Answer 2

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

Answer 3

The Gamma Function by James Bonner is a good read.It outlines the basics of the Gamma function with a bunch of different other functions and mathematical or physics techniques in an understanding manner.The author makes the terminology easily understandable and outlines the following such as Analytical continuation,The decaying expoential,the beta function,roduct and reflection formulas,digamma and polygamma functions,the zeta function,residues,Stirlings formula,Hankels Contour , Mittag - Lafleur Function and much more. It is a good read and I would highly recommend it as it outlines the versatility of the gamma function with other commen functions as well as mathematical techniques and uses of other methods in unison with the Gamma function and thier relations or motivation of its tehnique.The book also provides a series of good proofs for all theroms and collaries and examples.I think the best proof provided was the proofs in the Beta function, some of them are tedious bit some also have been omitted due to complexity and will inform the readaer when proof is not included due to complexity.There is a good proof in the Beta function to which extends to other chapters of the book with additional proof for the secondary or tertiary function such as with the decaying expoential or Holders Therom.