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46: Functional analysis


Functional analysis views the big picture in differential equations, for example, thinking of a differential operator as a linear map on a large set of functions. Thus this area becomes the study of (infinite-dimensional) vector spaces with some kind of metric or other structure, including ring structures (Banach algebras and C-* algebras for example). Appropriate generalizations of measure, derivatives, and duality also belong to this area.


See e.g. Jean Dieudonné, "History of Functional Analysis", North-Holland (Amsterdam) 1981

Applications and related fields

For manifolds modeled on topological linear spaces, See 57N20, 58BXX

Some questions about topological vector spaces are best stated a bit more generally in 54: General topology; in particular, vector spaces with a distance function, especially normed vector spaces or, more special yet, inner product spaces are examples of 54E: Metric spaces. [Schematic of subareas and related areas]


Browse all (old) classifications for this area at the AMS.

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