On the foundations of nonlinear generalized functions. I, II (Q2750969)
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scientific article; zbMATH DE number 1663212
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the foundations of nonlinear generalized functions. I, II |
scientific article; zbMATH DE number 1663212 |
Statements
21 October 2001
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Colombeau algebra
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diffeomorphism-invariant differential algebra of generalized functions of Colombeau type
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Schwartz distributions
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nonlinear theory of generalized functions
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differential geometry
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partial differential equations
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geometry
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relativity
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On the foundations of nonlinear generalized functions. I, II (English)
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A diffeomorphism-invariant differential algebra of generalized functions of Colombeau type \({\mathcal G}^d(\Omega)\) is constructed with a canonical copy of the sapce of Schwartz distributions \({\mathcal D}'(\Omega)\). The result is important for the nonlinear theory of generalized functions and for functional analysis in general. It opens the door to applications to differential geometry, partial differential equations with origin in geometry, and relativity theory.
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