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Zeitschrift für Analysis und ihre Anwendungen


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Volume 15, Issue 1, 1996, pp. 57–74
DOI: 10.4171/ZAA/688

Published online: 1996-03-31

A New Algebra of Periodic Generalized Functions

V. Valmorin[1]

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

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

Keywords: Periodic distributions, Fourier coefficients, periodic generalized functions, Colombeau algebras, differential problems with strong non-linearities

Valmorin V.: A New Algebra of Periodic Generalized Functions. Z. Anal. Anwend. 15 (1996), 57-74. doi: 10.4171/ZAA/688