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Isomorphisms of algebras of generalized functions

Hans Vernaeve (UGent)
(2011) MONATSHEFTE FUR MATHEMATIK. 162(2). p.225-237
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Abstract
We show that for smooth manifolds X and Y , any isomorphism between the algebras of generalized functions (in the sense of Colombeau) on X , resp. Y is given by composition with a unique generalized function from Y to X . We also characterize the multiplicative linear functionals from the Colombeau algebra on X to the ring of generalized numbers. Up to multiplication with an idempotent generalized number, they are given by an evaluation map at a compactly supported generalized point on X.
Keywords
Multiplicative linear functionals, Algebra homomorphisms, Composition operators, MICROLOCAL ANALYSIS, MANIFOLD, TOPOLOGICAL RING, DISTRIBUTIONS, SMOOTH FUNCTIONS, Nonlinear generalized functions

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Citation

Please use this url to cite or link to this publication:

MLA
Vernaeve, Hans. “Isomorphisms of Algebras of Generalized Functions.” MONATSHEFTE FUR MATHEMATIK 162.2 (2011): 225–237. Print.
APA
Vernaeve, H. (2011). Isomorphisms of algebras of generalized functions. MONATSHEFTE FUR MATHEMATIK, 162(2), 225–237.
Chicago author-date
Vernaeve, Hans. 2011. “Isomorphisms of Algebras of Generalized Functions.” Monatshefte Fur Mathematik 162 (2): 225–237.
Chicago author-date (all authors)
Vernaeve, Hans. 2011. “Isomorphisms of Algebras of Generalized Functions.” Monatshefte Fur Mathematik 162 (2): 225–237.
Vancouver
1.
Vernaeve H. Isomorphisms of algebras of generalized functions. MONATSHEFTE FUR MATHEMATIK. 2011;162(2):225–37.
IEEE
[1]
H. Vernaeve, “Isomorphisms of algebras of generalized functions,” MONATSHEFTE FUR MATHEMATIK, vol. 162, no. 2, pp. 225–237, 2011.
@article{1849929,
  abstract     = {{We show that for smooth manifolds X and Y , any isomorphism between the algebras of generalized functions (in the sense of Colombeau) on X , resp. Y is given by composition with a unique generalized function from Y to X . We also characterize the multiplicative linear functionals from the Colombeau algebra on X to the ring of generalized numbers. Up to multiplication with an idempotent generalized number, they are given by an evaluation map at a compactly supported generalized point on X.}},
  author       = {{Vernaeve, Hans}},
  issn         = {{0026-9255}},
  journal      = {{MONATSHEFTE FUR MATHEMATIK}},
  keywords     = {{Multiplicative linear functionals,Algebra homomorphisms,Composition operators,MICROLOCAL ANALYSIS,MANIFOLD,TOPOLOGICAL RING,DISTRIBUTIONS,SMOOTH FUNCTIONS,Nonlinear generalized functions}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{225--237}},
  title        = {{Isomorphisms of algebras of generalized functions}},
  url          = {{http://dx.doi.org/10.1007/s00605-009-0152-9}},
  volume       = {{162}},
  year         = {{2011}},
}

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