Algebras of generalized functions with smooth parameter dependence
2012 ◽
Vol 55
(1)
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pp. 105-124
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Keyword(s):
AbstractWe show that spaces of Colombeau generalized functions with smooth parameter dependence are isomorphic to those with continuous parametrization. Based on this result we initiate a systematic study of algebraic properties of the ring $\tilde{\mathbb{K}}_\mathrm{sm}$ of generalized numbers in this unified setting. In particular, we investigate the ring and order structure of $\tilde{\mathbb{K}}_\mathrm{sm}$ and establish some properties of its ideals.
2004 ◽
Vol 80
(2)
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pp. 123-174
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2012 ◽
Vol 388
(2)
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pp. 1166-1179
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2004 ◽
Vol 297
(2)
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pp. 456-471
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2008 ◽
Vol 138
(04)
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pp. 843-871
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1998 ◽
Vol 41
(1)
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pp. 47-60
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2012 ◽
Vol 10
(04)
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pp. 439-467
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2015 ◽
Vol 58
(3)
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pp. 717-738