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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.

  1. 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.

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  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
    • Lectures on Partial Differential Equations and Representations of Semigroups.

  2. Vector-Valued Distributions and Fourier Multipliers, by Herbert Amann, is freely available.
    A more extensive list of text books is at Good books on theory of distributions

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