About: Wiener–Hopf method

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The Wiener–Hopf method is a mathematical technique widely used in applied mathematics. It was initially developed by Norbert Wiener and Eberhard Hopf as a method to solve systems of integral equations, but has found wider use in solving two-dimensional partial differential equations with mixed boundary conditions on the same boundary. In general, the method works by exploiting the complex-analytical properties of transformed functions. Typically, the standard Fourier transform is used, but examples exist using other transforms, such as the Mellin transform.

Attributes	Values
rdf:type	topical concept
rdfs:label	Wiener–Hopf method (en)
rdfs:comment	The Wiener–Hopf method is a mathematical technique widely used in applied mathematics. It was initially developed by Norbert Wiener and Eberhard Hopf as a method to solve systems of integral equations, but has found wider use in solving two-dimensional partial differential equations with mixed boundary conditions on the same boundary. In general, the method works by exploiting the complex-analytical properties of transformed functions. Typically, the standard Fourier transform is used, but examples exist using other transforms, such as the Mellin transform. (en)
sameAs	Wiener–Hopf method
dbp:wikiPageUsesTemplate	dbt:Citation_needed dbt:Cite_book dbt:Cite_web dbt:Math dbt:Mvar dbt:SpringerEOM
Subject	Partial differential equations
gold:hypernym	Technique
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Wiener–Hopf_method?oldid=993447548&ns=0
Wikipage page ID	4363034 (xsd:integer)
page length (characters) of wiki page	7425 (xsd:nonNegativeInteger)
Wikipage revision ID	993447548 (xsd:integer)
has abstract	The Wiener–Hopf method is a mathematical technique widely used in applied mathematics. It was initially developed by Norbert Wiener and Eberhard Hopf as a method to solve systems of integral equations, but has found wider use in solving two-dimensional partial differential equations with mixed boundary conditions on the same boundary. In general, the method works by exploiting the complex-analytical properties of transformed functions. Typically, the standard Fourier transform is used, but examples exist using other transforms, such as the Mellin transform. In general, the governing equations and boundary conditions are transformed and these transforms are used to define a pair of complex functions (typically denoted with '+' and '−' subscripts) which are respectively analytic in the upper and lower halves of the complex plane, and have growth no faster than polynomials in these regions. These two functions will also coincide on some region of the complex plane, typically, a thin strip containing the real line. Analytic continuation guarantees that these two functions define a single function analytic in the entire complex plane, and Liouville's theorem implies that this function is an unknown polynomial, which is often zero or constant. Analysis of the conditions at the edges and corners of the boundary allows one to determine the degree of this polynomial. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Wiener–Hopf_method
is Wikipage redirect of	Wiener-Hopf factorisation Wiener-Hopf method Wiener-hopf Wiener-Hopf Wiener-Hopf equation Wiener-Hopf equations Wiener-Hopf factorization Wiener-Hopf problem Wiener–Hopf Wiener–Hopf equation Wiener–Hopf equations Wiener–Hopf factorisation Wiener–Hopf factorization Wiener–Hopf problem
is Link from a Wikipage to another Wikipage of	List of things named after Norbert Wiener Adaptive filter Gigla Janashia David Abrahams (mathematician) David Williams (mathematician) Cindy Greenwood Lindley equation List of partial differential equation topics Eberhard Hopf G/G/1 queue Harold Widom Kosambi–Karhunen–Loève theorem Ladder height process Klein–Kramers equation Lawrence Sirovich

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