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Functional Analysis is a division of Mathematical Analysis, which deals with functions of functions. The major concentration of Functional Analysis is on the study of vector spaces and linear functions. It developed as a definite field over the last few decades, after it was identified that various mathematical processes starting from arithmetic to calculus systems, manifest substantially similar characteristics. A functional is a correlation between things, but the things are mathematical numbers, vectors, or functions. Spaces are known as the groupings of such things. Differentiation portrays a relationship of one function with another function (the derivative) and hence is an example of a function. Integration is a function too. The functional Analysis concentrates on groups of functions, like the ones that are capable of being differentiated or integrated. Functional Analysis began by studying the spaces of functions, but it has proven to be very useful in the study of differential equations and Integral equations. An essential component of functional Analysis is the branch of the theory of measure, integration, and probability to infinite-dimensional spaces, also known as infinite-dimensional Analysis.
1. Hilbert Spaces
2. Branch Spaces
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