Editing Mathematical analysis (section)

=== Functional analysis ===
{{Main|Functional analysis}}
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of [[vector space]]s endowed with some kind of limit-related structure (e.g. [[Inner product space#Definition|inner product]], [[Norm (mathematics)#Definition|norm]], [[Topological space#Definitions|topology]], etc.) and the [[linear transformation|linear operators]] acting upon these spaces and respecting these structures in a suitable sense.<ref name="Rudin_1991"/><ref name="Conway_1994"/> The historical roots of functional analysis lie in the study of [[function space|spaces of functions]] and the formulation of properties of transformations of functions such as the [[Fourier transform]] as transformations defining [[continuous function|continuous]], [[unitary operator|unitary]] etc. operators between function spaces.  This point of view turned out to be particularly useful for the study of [[differential equations|differential]] and [[integral equations]].