The History of Functional Analysis:From Vito Volterra to John von Neumann
Functional analysis is a subject which uses algebraic and geometric ideas and methods to study problems in analytics.Volterra's work on functional theory laid the prerequisites for Fréchet's creation of the theory of abstract metric spaces.Volterra was also the first to reveal the implied similarity between integral equations and systems of linear equations.Fredholm's successful extension of the theory of systems of linear equations to continuous kernel integral equations was a successful example of the use of algebraic ideas and methods to solve analytic problems,which inspired the construction of Hilbert's framework for the unification of analysis and algebra.In line with the trend towards abstraction in mathematics in the 20th century,Hilbert's followers introduced geometric concepts and established functional analysis in the reformulation and development of the idea of Hilbert's integral equations.
history of modern mathematicsfunctional analysisintegral equationcalculus of variationslinear system of equations
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