Q: Is there a set of some comprehensive surveys or monographs describing (in
technical detail) the historical development of the various
subareas of analysis and partial differential equations?
I'm especially (but not only) interested in expositions of the most recent ($20^{\text{th}}$ century onwards) developments.
For instance, I already know the following works:
- History of Functional Analysis, by J. Dieudonné;
- Partial Differential Equations in the 20th Century, by H. Brezis and F. Browder;
- A History of Analysis, edited by H. N. Jahnke.
A slight variation on the theme of this question is:
Q': Which "texbooks"/monographs (dealing with subareas of analysis and PDE) strongly embrace an historical point of view?
For example, I've some good memories of the following book (which deals with topics in basic calculus):
- Analysis by Its History by E. Hairer and G. Wanner.
A quite related question is Motivation for and history of pseudo-differential operators.
Best Answer
If you are interested in the history of Banach space geometry, then the monograph
Pietsch: History of Banach spaces and linear operators
is a good reference, even if it reflects at places the personal taste of the author.
About Sobolev spaces and this direction of PDE's, besides your references the book
Tartar: An Introduction to Sobolev Spaces and Interpolation Spaces
contains plenty of historical remarks and references.