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 operators acting upon these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of
spaces of functions and the formulation of properties of transformations of functions such as the
Fourier transform as transformations defining
continuous,
unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of
differential and
integral equations.