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The classical theory of calculus of variations for generalized functions
Alexander Lecke, Lorenzo Luperi Baglini, Paolo Giordano
We present an extension of the classical theory of calculus of variations to generalized functions. The framework is the category of generalized smooth functions, which includes Sc…
Asymptotic gauges: generalization of Colombeau type algebras
Paolo Giordano, Lorenzo Luperi Baglini
We use the general notion of set of indices to construct algebras of nonlinear generalized functions of Colombeau type. They are formally defined in the same way as the special Col…
Generalized Functions Beyond Distributions
Vieri Benci, Lorenzo Luperi Baglini
Ultrafunctions are a particular class of functions defined on a Non Archimedean field R^{*}\supset R. They have been introduced and studied in some previous works ([1],[2],[3]). In…
A non-archimedean Algebra and the Schwartz impossibility theorem
Vieri Benci, Lorenzo Luperi Baglini
In the 1950s L. Schwartz proved his famous impossibility result: for every k in N there does not exist a differential algebra (A,+,*,D) in which the distributions can be embedded,…