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[Functional-analytic areas of MathMap]

Theory of Functions and related areas

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Here we mean the study of vector spaces of functions. This can include the abstract study of topological vector spaces as well as the study of particular spaces of interest, including attention to their bases (e.g. Fourier Analysis), and linear maps on them (e.g. Integral Transforms).

Also highlighted on the MathMap is 22: Topological Groups since, in practice, a good deal of material in that area is concerned with Harmonic Analysis -- the study of special (bases of) functions on Lie Groups.

Clearly related to this topic are several of the fields of classical analysis and calculus, such as 39: Functional Equations and 33: Special Functions. We have (somewhat arbitrarily) grouped the fields in this area together because of the emphasis on the vector-space perspective.

You might want to continue the tour with a trip through differential equations.


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Last modified 2000/01/25 by Dave Rusin. Mail: