About: Weil–Brezin Map

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In mathematics, the Weil–Brezin map, named after André Weil and Jonathan Brezin, is a unitary transformation that maps a Schwartz function on the real line to a smooth function on the Heisenberg manifold. The Weil–Brezin map gives a geometric interpretation of the Fourier transform, the Plancherel theorem and the Poisson summation formula. The image of Gaussian functions under the Weil–Brezin map are nil-theta functions, which are related to theta functions. The Weil–Brezin map is sometimes referred to as the Zak transform, which is widely applied in the field of physics and signal processing; however, the Weil–Brezin Map is defined via Heisenberg group geometrically, whereas there is no direct geometric or group theoretic interpretation from the Zak transform.

Attributes	Values
rdf:type	programming language
rdfs:label	Weil–Brezin Map (en)
rdfs:comment	In mathematics, the Weil–Brezin map, named after André Weil and Jonathan Brezin, is a unitary transformation that maps a Schwartz function on the real line to a smooth function on the Heisenberg manifold. The Weil–Brezin map gives a geometric interpretation of the Fourier transform, the Plancherel theorem and the Poisson summation formula. The image of Gaussian functions under the Weil–Brezin map are nil-theta functions, which are related to theta functions. The Weil–Brezin map is sometimes referred to as the Zak transform, which is widely applied in the field of physics and signal processing; however, the Weil–Brezin Map is defined via Heisenberg group geometrically, whereas there is no direct geometric or group theoretic interpretation from the Zak transform. (en)
dcterms:subject	Harmonic analysis Representation theory
Wikipage page ID	43178654 (xsd:integer)
Wikipage revision ID	1052365877 (xsd:integer)
Link from a Wikipage to another Wikipage	Canonical commutation relation Unitary operator Lie group Zak transform Harmonic analysis Mathematics Eigenspace Entire function Gaussian function Theta function Oscillator representation André Weil Lie algebra Signal processing Stone–von Neumann theorem Physics Automorphism Haar measure Heisenberg group Irreducible representation Fourier transform Nilpotent Lie algebra Nilpotent group Differential operator Graded ring Pointwise convergence Isomorphic Finite Fourier transform (disambiguation) Nilmanifold Representation theory Kernel (linear algebra) Theta representation Unitary transformation Poisson summation formula Schwartz function Unitary representation Square-integrable function Plancherel theorem Quotient manifold Jacobi theta function Weil representation
sameAs	Weil–Brezin Map Weil–Brezin Map Weil–Brezin Map
dbp:wikiPageUsesTemplate	dbt:Orphan dbt:Reflist
has abstract	In mathematics, the Weil–Brezin map, named after André Weil and Jonathan Brezin, is a unitary transformation that maps a Schwartz function on the real line to a smooth function on the Heisenberg manifold. The Weil–Brezin map gives a geometric interpretation of the Fourier transform, the Plancherel theorem and the Poisson summation formula. The image of Gaussian functions under the Weil–Brezin map are nil-theta functions, which are related to theta functions. The Weil–Brezin map is sometimes referred to as the Zak transform, which is widely applied in the field of physics and signal processing; however, the Weil–Brezin Map is defined via Heisenberg group geometrically, whereas there is no direct geometric or group theoretic interpretation from the Zak transform. (en)
gold:hypernym	Transformation
prov:wasDerivedFrom	wikipedia-en:Weil–Brezin_Map?oldid=1052365877&ns=0
page length (characters) of wiki page	12633 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Weil–Brezin_Map
is Link from a Wikipage to another Wikipage of	André Weil List of things named after André Weil Weil-Brezin Map
is Wikipage redirect of	Weil-Brezin Map
is known for of	André Weil
is foaf:primaryTopic of	wikipedia-en:Weil–Brezin_Map

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