9 citations · 16 across the 5 of their papers we have counts for
9 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…
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…
First-order hyperbolic pseudodifferential equations with generalized symbols
Guenther Hoermann
We consider the Cauchy problem for a hyperbolic pseudodifferential operator whose symbol is generalized, resembling a representative of a Colombeau generalized function. Such equat…
Microlocal hypoellipticity of linear partial differential operators with generalized functions as coefficients
Guenther Hoermann, Michael Oberguggenberger, Stevan Pilipovic
We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalize…
Elliptic regularity and solvability for partial differential equations with Colombeau coefficients
Guenther Hoermann, Michael Oberguggenberger
The paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constant…
Hölder-Zygmund regularity in algebras of generalized functions
Guenther Hoermann
We introduce an intrinsic notion of Hoelder-Zygmund regularity for Colombeau generalized functions. In case of embedded distributions belonging to some Zygmund-Hoelder space this i…