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In mathematics, a progressive function ''ƒ'' ∈ ''L''2(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 line will arise in this manner. Regressive functions are similarly associated with the Hardy space on the lower half-plane . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「progressive function」の詳細全文を読む スポンサード リンク
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