functional analysis


functional analysis
the branch of mathematics that deals with the theory of vector spaces and linear functionals.
[1945-50]

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Branch of mathematical analysis dealing with functionals, or functions of functions.

It emerged as a distinct field in the 20th century, when it was realized that diverse mathematical processes, from arithmetic to calculus procedures, exhibit very similar properties. A functional, like a function, is a relationship between objects, but the objects may be numbers, vectors, or functions. Groupings of such objects are called spaces. Differentiation is an example of a functional because it defines a relationship between a function and another function (its derivative). Integration is also a functional. Functional analysis focuses on classes of functions, such as those that can be differentiated or integrated.

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Universalium. 2010.

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