progressive function

Definition

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

$$supp\widehat{f}\subseteq {ℝ}_{+}.$$

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

$$supp\widehat{f}\subseteq {ℝ}_{-}.$$

Title	progressive function
Canonical name	ProgressiveFunction
Date of creation	2013-03-22 14:28:20
Last modified on	2013-03-22 14:28:20
Owner	swiftset (1337)
Last modified by	swiftset (1337)
Numerical id	4
Author	swiftset (1337)
Entry type	Definition
Classification	msc 42A99
Related topic	FourierTransform
Defines	regressive function