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progressive function (Definition)

Definition

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

$\displaystyle \ensuremath{\mathop{\rm supp}}\hat{f} \subseteq \ensuremath{\mathbb{R}}_+.$
It is called regressive iff the time reversed function $f(-t)$ is progressive, or equivalently, if

$\displaystyle \ensuremath{\mathop{\rm supp}}\hat{f} \subseteq \ensuremath{\mathbb{R}}_-.$



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See Also: Fourier transform

Also defines:  regressive function
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Cross-references: positive, Fourier transform, iff, progressive, function

This is version 1 of progressive function, born on 2004-07-11.
Object id is 5993, canonical name is ProgressiveFunction.
Accessed 2636 times total.

Classification:
AMS MSC: 42A99 (Fourier analysis :: Fourier analysis in one variable :: Miscellaneous)
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