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- Progressive_function abstract "In mathematics, a progressive function ƒ ∈ L2(R) is a function whose Fourier transform is supported by positive frequencies only:It is called super regressive if and only if the time reversed function f(−t) is progressive, or equivalently, ifThe complex conjugate of a progressive function is regressive, and vice versa.The space of progressive functions is sometimes denoted , which is known as the Hardy space of the upper half-plane. This is because a progressive function has the Fourier inversion formulaand hence extends to a holomorphic function on the upper half-plane by the formulaConversely, every holomorphic function on the upper half-plane which is uniformly square-integrable on every horizontal linewill 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.".
- Progressive_function wikiPageID "1461442".
- Progressive_function wikiPageRevisionID "536710238".
- Progressive_function hasPhotoCollection Progressive_function.
- Progressive_function id "5993".
- Progressive_function title "progressive function".
- Progressive_function subject Category:Hardy_spaces.
- Progressive_function subject Category:Types_of_functions.
- Progressive_function type Abstraction100002137.
- Progressive_function type Attribute100024264.
- Progressive_function type HardySpaces.
- Progressive_function type Space100028651.
- Progressive_function comment "In mathematics, a progressive function ƒ ∈ L2(R) is a function whose Fourier transform is supported by positive frequencies only:It is called super regressive if and only if the time reversed function f(−t) is progressive, or equivalently, ifThe complex conjugate of a progressive function is regressive, and vice versa.The space of progressive functions is sometimes denoted , which is known as the Hardy space of the upper half-plane.".
- Progressive_function label "Progressive function".
- Progressive_function sameAs m.053cy4.
- Progressive_function sameAs Q7248844.
- Progressive_function sameAs Q7248844.
- Progressive_function sameAs Progressive_function.
- Progressive_function wasDerivedFrom Progressive_function?oldid=536710238.
- Progressive_function isPrimaryTopicOf Progressive_function.