Weak Topology (polar topology)
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High Quality Content by WIKIPEDIA articles! Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of vector spaces and operators acting upon them. It has its historical roots in the study of functional spaces, in particular transformations of functions, such as the Fourier transform, as well as in the study of differential and integral equations. This usage of the word functional goes back to the calculus of variations, implying a function whose argument is a function. Its use in general has been attributed to Italian mathematician and physici...
High Quality Content by WIKIPEDIA articles! Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of vector spaces and operators acting upon them. It has its historical roots in the study of functional spaces, in particular transformations of functions, such as the Fourier transform, as well as in the study of differential and integral equations. This usage of the word functional goes back to the calculus of variations, implying a function whose argument is a function. Its use in general has been attributed to Italian mathematician and physicist Vito Volterra and its founding is largely attributed to a group of Polish mathematicians around Stefan Banach. In the modern view, functional analysis is seen as the study of vector spaces endowed with a topology, in particular infinite dimensional spaces. In contrast, linear algebra deals mostly with finite dimensional spaces, or does not use topology. An important part of functional analysis is the extension of the theory of measure, integration, and probability to infinite dimensional spaces, also known as infinite dimensional analysis.
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