Linear Differential Equations and the Sturm-Liouville Problem. The ``Crypto-Integral'' Equations. The Equation of Vibrating Membranes. The Idea of Infinite Dimension. The Crucial Years and the Definition of Hilbert Space. Duality and the Definition of Normed Spaces. Spectral Theory after 1900. Locally Convex Spaces and the Theory of Distributions. Applications of Functional Analysis to Differential and Partial Differential Equations. References. Author and Subject Index.
An excellent supplement to any standard course in functional analysis. American Mathematical Monthly The admirable book under review, written by an eminently qualified mathematician, makes a notable contribution to the understanding of the historical process that has shaped what is known today as functional analysis...Dieudonne has given us a very readable and exciting account of how functional analysis has evolved...This is essential reading for functional analysts who wish to know how their subject came into existence. Bulletin of the American Mathematical Society