Microlocal analysis in the dual of a Colombeau algebra: generalized wave front sets and noncharacteristic regularity.
Sufficient conditions of local solvability for partial differential operators on spaces of Colombeau type.
On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets.
Pseudodifferential operators with generalized symbols and regularity theory.
- and -hypoellipticity of partial differential operators with constant Colombeau coefficients
We provide a deep investigation of the notions of - and -hypoellipticity for partial differential operators with constant Colombeau coefficients. This involves generalized polynomials and fundamental solutions in the dual of a Colombeau algebra. Sufficient conditions and necessary conditions for - and -hypoellipticity are given
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