In mathematics, a progressive function ƒ ∈ L2(R) is a function whose Fourier transform is supported by positive frequencies only:[1] It is called super regressive if and only if the time reversed function f(−t) is progressive, or equivalently, if The complex conjugate of a progressive function is regressive, and vice versa.
This is because a progressive function has the Fourier inversion formula and hence extends to a holomorphic function on the upper half-plane
by the formula Conversely, every holomorphic function on the upper half-plane which is uniformly square-integrable on every horizontal line will arise in this manner.
Regressive functions are similarly associated with the Hardy space on the lower half-plane
This article incorporates material from progressive function on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.