A new algebra of periodic generalized functions (Q1909643)

Summary: 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 \({\mathcal D}^{\prime(n)}_{2\pi}\) 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 \({\mathcal D}^{\prime(n)}_{2\pi}\).