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replacing redirect Holomorphic to dab page with appropriate destination Holomorphic function |
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In [[mathematics]], a '''progressive function''' ''ƒ'' ∈ ''L''<sup>2</sup>('''R''') is a function whose [[Fourier transform]] is supported by positive frequencies only:<ref>{{cite book |last1=Klees |first1=Roland |last2=Haagmans |first2=Roger |title=Wavelets in the Geosciences |date=6 March 2000 |publisher=Springer Science & Business Media |isbn=978-3-540-66951-7 |url=https://books.google.com/books?id=6-xW6Bo-UA8C&dq=%22Progressive+function%22+-wikipedia+Fourier+transform&pg=PA13 |language=en}}</ref>
:<math>\mathop{\rm supp}\hat{f} \subseteq \mathbb{R}_+.</math>
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Regressive functions are similarly associated with the Hardy space on the lower half-plane <math>\{ t + iu: t, u \in R, u \leq 0 \}</math>.
==References==
{{reflist}}
{{PlanetMath attribution|id=5993|title=progressive function}}
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