3 citations · 4 across the 5 of their papers we have counts for
5 papers
On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets
Claudia Garetto, Guenther Hoermann
Summarizing basic facts from abstract topological modules over Colombeau generalized complex numbers we discuss duality of Colombeau algebras. In particular, we focus on generalize…
Pseudo-differential operators in algebras of generalized functions and global hypoellipticity
Claudia Garetto
The aim of this work is to develop a global calculus for pseudo-differential operators acting on suitable algebras of generalized functions. In particular, a condition of global hy…
Topological structures in Colombeau algebras: investigation of the duals of $\Gc(\Om)$, $\G(\Om)$ and $\GS(\R^n)$
Claudia Garetto
We study the topological duals of the Colombeau algebras $\Gc(\Om)$, $\G(\Om)$ and $\GS(\R^n)$, discussing some continuous embeddings and the properties of generalized delta functi…
Topological structures in Colombeau algebras: topological $\widetilde{\C}$-modules and duality theory
Claudia Garetto
We study modules over the ring $\widetilde{\C}$ of complex generalized numbers from a topological point of view, introducing the notions of $\widetilde{\C}$-linear topology and loc…
Microlocal analysis of generalized functions: pseudodifferential techniques and propagation of singularities
Claudia Garetto, Guenther Hoermann
We characterize microlocal regularity of Colombeau generalized functions by an appropriate extension of the classical notion of micro-ellipticity to pseudodifferential operators wi…