functional analysis is primarily concerned with infinite-dimensional linear(vector) spaces, mainly function spaces whose "points" are functions, andmappings between them, usually called operators or, functionals if the rangeis on the real line or in the complex plane. it was invented and developedin the last years of the nineteenth century and the first few decades of thetwentieth century. during the early period of its development, the originalpurpose of functional analysis was to use a framework which allows the studyof differential and integral equations to be considered in the same formulation(cf. [6]). later, functional analysis developed rapidly as in-depth study and in-terconnection on spectral theory of ordinary and partial differential equations,potential theory, fourier expansions, and applied mathematical techniques,especially, on the influence of mathematical physics and quantum mechan-ics.
