1. An existence and uniqueness result about algebras of Schwartz distributions.
- Author
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Dias, Nuno Costa, Jorge, Cristina, and Prata, João Nuno
- Abstract
We prove that there exists essentially one minimal differential algebra of distributions A , satisfying all the properties stated in the Schwartz impossibility result [L. Schwartz, Sur l'impossibilité de la multiplication des distributions, 1954], and such that C p ∞ ⊆ A ⊆ D ′ (where C p ∞ is the set of piecewise smooth functions and D ′ is the set of Schwartz distributions over R ). This algebra is endowed with a multiplicative product of distributions, which is a generalization of the product defined in [N.C.Dias, J.N.Prata, A multiplicative product of distributions and a class of ordinary differential equations with distributional coefficients, 2009]. If the algebra is not minimal, but satisfies the previous conditions, is closed under anti-differentiation and the dual product by smooth functions, and the distributional product is continuous at zero then it is necessarily an extension of A . [ABSTRACT FROM AUTHOR]
- Published
- 2024
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