# progressive function

## Definition

A function $f\in L^{2}(\mathbb{R})$ is called progressive iff its Fourier transform is supported by positive frequencies only:

 $\mathop{\rm supp}\hat{f}\subseteq\mathbb{R}_{+}.$

It is called regressive iff the time reversed function $f(-t)$ is progressive, or equivalently, if

 $\mathop{\rm supp}\hat{f}\subseteq\mathbb{R}_{-}.$
Title progressive function ProgressiveFunction 2013-03-22 14:28:20 2013-03-22 14:28:20 swiftset (1337) swiftset (1337) 4 swiftset (1337) Definition msc 42A99 FourierTransform regressive function