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arXiv · 1507.02413

The category of Colombeau algebras

Lorenzo Luperi Baglini·Paolo Giordano
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Abstract

In [11], we introduced the notion of asymptotic gauge (AG), and we used it to construct Colombeau AG-algebras. This construction concurrently generalizes that of many different algebras used in Colombeau's theory, e.g. the special one $\mathcal{G}^{\srm}$, the full one $\gse$, the NSA based algebra of asymptotic functions $\hat{\mathcal{G}}$, and the diffeomorphism invariant algebras $\gsd$, $\mathcal{G}^{2}$ and $\hat{\mathcal{G}}$. In this paper we study the categorical properties of the construction of Colombeau AG-algebras with respect to the choice of the AG, and we show their consequences regarding the solvability of generalized ODE.

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Lorenzo Luperi Baglini, Paolo Giordano. 2015-07-09. The category of Colombeau algebras. https://arxiv.org/abs/1507.02413

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