Colombeau algebra (Q5147873)

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commutative associative differential algebra of generalized functions into which smooth functions (but not arbitrary continuous ones) embed as a subalgebra and distributions embed as a subspace

Language	Label	Description	Also known as
English	Colombeau algebra	commutative associative differential algebra of generalized functions into which smooth functions (but not arbitrary continuous ones) embed as a subalgebra and distributions embed as a subspace

Statements

commutative ring

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algebra over a field

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Jean-François Colombeau

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mathematical analysis

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discoverer or inventor

Jean-François Colombeau

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time of discovery or invention

1984

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defining formula

{\begin{aligned}H&=\{f(-,-)\colon M_{0}\to {\mathcal {C}}^{\infty }\}\\M_{p}&=\left\{\eta \in D\colon \int \eta (x)\,dx=1,\;\int \eta (x)x^{q}\,dx=0\;\forall q\in \{1,\dotsc ,p\}\right\}\\E&=\{f\in H\colon \exists p\forall \eta \in M_{0}\colon f(\eta _{\epsilon },x)=O(\epsilon ^{-p})\}\\N&=\{f\in H\colon \forall p\exists q\forall \eta \in M_{q}\colon f(\eta _{\epsilon },x)=O(\epsilon ^{p})\}\\G&=E/N\end{aligned}}

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

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Microsoft Academic ID

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Colombeau algebra

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Sitelinks

Wikipedia(1 entry)

enwiki Colombeau algebra

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