I am interested in systematically studying the theory of vector-valued distributions. The original two papers due to Laurent Schwartz entitled *Théorie des distributions à valeurs vectorielles. I & II* (1957-58) are written in French. Occasionally I have read mathematics papers in French when needed, with the help of Google Translate. But these papers are to the tune of 350-odd pages making it infeasible for such an undertaking.


1. Is there an English translation of these seminal papers by Schwartz?


The closest I have seen to a systematic exposition of vector-valued distributions is the book *Vector-valued distributions and Fourier multipliers* (<http://user.math.uzh.ch/amann/files/distributions.ps>) by Herbert Amann. But here some results are presented without proof and the reader is referred to Schwartz's papers. This brings me to my next question.


2. Is there a standard textbook (in English) which gives a self-contained account of the theory of vector-valued distributions?


What I am looking for is something like a vector-valued version of the series of books on Generalized Functions by Gelfand and Shilov (which had been promptly translated from Russian to English).


Thank you.



English translation of Schwartz's papers on vector-valued distributions
1. These papers have not been translated, as far as I know, however there exist lecture notes in english of courses by Schwarz on this topic:  

•  [Introduction to the Theory of Distributions](https://www.jstor.org/stable/10.3138/j.ctt1vxmd4v)  

• [Lectures on Partial Differential Equations and Representations of Semigroups](https://archive.org/details/L_Schwartz___Lectures_on_Partial_Differential_Equations_and_Representations_of_Semigroups).
2. [Vector-Valued Distributions and Fourier Multipliers](http://user.math.uzh.ch/amann/files/distributions.ps), by Herbert Amann, is freely available.  

A more extensive list of text books is at [Good books on theory of distributions](https://mathoverflow.net/q/20314/11260)


