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What is functional analysis in mathematics?

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Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. read more

Functional analysis, 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. read more

The application of functional analysis in mathematical and theoretical physics. Below, those branches of mathematical physics are given in which some part of functional analysis is applied. 1) The spectral theory of operators is applied in all theories of quantum physics: in quantum -body theory, in quantum field theory and in quantum statistical mechanics. read more

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Introduction to Functional Analysis | Mathematics | MIT ...
Source: ocw.mit.edu

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Encyclopedia of Mathematics
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