Editing Integral transform (section)

==General theory==
Although the properties of integral transforms vary widely, they have some properties in common. For example, every integral transform is a [[linear operator]], since the integral is a linear operator, and in fact if the kernel is allowed to be a [[generalized function]] then all linear  operators are integral transforms (a properly formulated version of this statement is the [[Schwartz kernel theorem]]).

The general theory of such [[integral equation]]s is known as [[Fredholm theory]].  In this theory, the kernel is understood to be a [[compact operator]] acting on a [[Banach space]] of functions. Depending on the situation, the kernel is then variously referred to as the [[Fredholm operator]], the [[nuclear operator]] or the [[Fredholm kernel]].