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- W4387156736 abstract "We prove that there exists essentially one {it minimal} differential algebra of distributions $A$, satisfying all the properties stated in the Schwartz impossibility result [L. Schwartz, Sur l'impossibilit'e de la multiplication des distributions, 1954], and such that $C_p^{infty} subseteq A subseteq DO' $ (where $C_p^{infty}$ is the set of piecewise smooth functions and $DO'$ is the set of Schwartz distributions over $RE$). 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 $A$." @default.
- W4387156736 created "2023-09-30" @default.
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- W4387156736 date "2023-09-25" @default.
- W4387156736 modified "2023-09-30" @default.
- W4387156736 title "An existence and uniqueness result about algebras of Schwartz distributions" @default.
- W4387156736 doi "https://doi.org/10.48550/arxiv.2309.14444" @default.
- W4387156736 hasPublicationYear "2023" @default.
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