About: Progressive function

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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, if The 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 formula and hence extends to a holomorphic function on the upper half-plane by the formula

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  • 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, if The 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 formula and hence extends to a holomorphic function on the upper half-plane by the formula Conversely, 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. (en)
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  • progressive function (en)
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  • 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, if The 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 formula and hence extends to a holomorphic function on the upper half-plane by the formula (en)
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  • Progressive function (en)
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