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In mathematics, a tube domain is a generalization of the notion of a vertical strip (or half-plane) in the complex plane to several complex variables. A strip can be thought of as the collection of complex numbers whose real part lie in a given subset of the real line and whose imaginary part is unconstrained; likewise, a tube is the set of complex vectors whose real part is in some given collection of real vectors, and whose imaginary part is unconstrained.

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rdf:type	yago:WikicatSeveralComplexVariables yago:PhysicalEntity100001930 yago:Thing100002452 yago:Variable109468959
rdfs:label	Tube domain (en)
rdfs:comment	In mathematics, a tube domain is a generalization of the notion of a vertical strip (or half-plane) in the complex plane to several complex variables. A strip can be thought of as the collection of complex numbers whose real part lie in a given subset of the real line and whose imaginary part is unconstrained; likewise, a tube is the set of complex vectors whose real part is in some given collection of real vectors, and whose imaginary part is unconstrained. (en)
dcterms:subject	Fourier analysis Harmonic analysis Several complex variables
Wikipage page ID	30270129 (xsd:integer)
Wikipage revision ID	1109050557 (xsd:integer)
Link from a Wikipage to another Wikipage	Fourier analysis Holomorphic function Relativity theory Complex number Complex plane Convex set Harmonic analysis Several complex variables Mathematics Encyclopedia of Mathematics Minkowski space Convex hull Bergman metric Hardy space Domain of a function Domain of holomorphy Quantum gravity Internet Archive Arithmetic Laplace transform Half-plane Open set Real coordinate space Real number Real part Complex coordinate space European Mathematical Society Reinhardt domain Monge cone Paley–Wiener theorem Siegel domain Dual cone Siegel half-space Null cone Bounded symmetric domain Holomorphically convex dbr:Future_tube dbr:Holomorphic_envelope dbr:Multidimensional_Laplace_transform
Link from a Wikipage to an external page	https://archive.org/details/introductiontofo0000stei https://encyclopediaofmath.org/index.php%3Ftitle=Tube_domain
sameAs	Tube domain Tube domain Tube domain Tube domain
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has abstract	In mathematics, a tube domain is a generalization of the notion of a vertical strip (or half-plane) in the complex plane to several complex variables. A strip can be thought of as the collection of complex numbers whose real part lie in a given subset of the real line and whose imaginary part is unconstrained; likewise, a tube is the set of complex vectors whose real part is in some given collection of real vectors, and whose imaginary part is unconstrained. Tube domains are domains of the Laplace transform of a function of several real variables (see ). Hardy spaces on tubes can be defined in a manner in which a version of the Paley–Wiener theorem from one variable continues to hold, and characterizes the elements of Hardy spaces as the Laplace transforms of functions with appropriate integrability properties. Tubes over convex sets are domains of holomorphy. The Hardy spaces on tubes over convex cones have an especially rich structure, so that precise results are known concerning the boundary values of Hp functions. In mathematical physics, the is the tube domain associated to the interior of the past null cone in Minkowski space, and has applications in relativity theory and quantum gravity. Certain tubes over cones support a Bergman metric in terms of which they become bounded symmetric domains. One of these is the Siegel half-space which is fundamental in arithmetic. (en)
gold:hypernym	Generalization
prov:wasDerivedFrom	wikipedia-en:Tube_domain?oldid=1109050557&ns=0
page length (characters) of wiki page	6978 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Tube_domain
is Link from a Wikipage to another Wikipage of	Bochner's tube theorem Hardy space Symmetric cone Tube Siegel domain
is Wikipage disambiguates of	Tube
is foaf:primaryTopic of	wikipedia-en:Tube_domain

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