# progressive function

## Definition

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

$$supp\widehat{f}\subseteq {\mathbb{R}}_{+}.$$ |

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

$$supp\widehat{f}\subseteq {\mathbb{R}}_{-}.$$ |

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 |