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where the contours <math>C_1</math> and <math>C_2</math> are parallel to the real line, but pass above and below the point <math>z=\alpha</math>, respectively.
Similarly, arbitrary scalar functions may be decomposed into a product of +/− functions, i.e. <math>K(\alpha) = K_+(\alpha)K_-(\alpha)</math>, by first taking the logarithm, and then performing a sum decomposition. Product decompositions of matrix functions (which occur in coupled multi-modal systems such as elastic waves) are considerably more problematic since the logarithm is not well defined, and any decomposition might be expected to be non-commutative. A small subclass of commutative decompositions were obtained by Khrapkov, and various approximate methods have also been developed.{{citation needed}}
==Example==
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* [[Wiener filter]]
==
* {{SpringerEOM |id=W/w097910}}▼
* {{Cite web|title=Category:Wiener-Hopf - WikiWaves|url=https://wikiwaves.org/Category:Wiener-Hopf|website=wikiwaves.org|access-date=2020-05-19}}
▲* {{SpringerEOM |id=W/w097910|title=Wiener-Hopf method}}
* {{Cite book|last=Fornberg, Bengt,|url=https://www.worldcat.org/oclc/1124781689|title=Complex variables and analytic functions : an illustrated introduction|others=Piret, Cécile,|isbn=978-1-61197-597-0|___location=Philadelphia|oclc=1124781689}}
{{DEFAULTSORT:Wiener-Hopf method}}
[[Category:Partial differential equations]]
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