A New Algebra of Periodic Generalized Functions

  • V. Valmorin

    Université des Antilles et de la Guyane, Pointe-à-Pitre, Guadeloupe


Let nn denote a strictly positive integer. We construct a complex differential algebra Gn\mathcal G_n of so-called 2π2\pi-periodic generalized functions. We show that the space D2π(n)\mathcal D^{'(n)}_{2\pi} of 2π2\pi-periodic distributions on Rn\mathbb R^n can be canonically embedded into Gn\mathcal G_n. Next we lay the foundation for calculation in Gn\mathcal G_n. This algebra Gn\mathcal G_n enables one to solve, in a canonical way, differential problems with strong singular periodic data which have no solution in D2π(n)\mathcal D^{'(n)}_{2\pi}.

Cite this article

V. Valmorin, A New Algebra of Periodic Generalized Functions. Z. Anal. Anwend. 15 (1996), no. 1, pp. 57–74

DOI 10.4171/ZAA/688