New York Journal of Mathematics
Volume 12 (2006) 275-318


Claudia Garetto

Microlocal analysis in the dual of a Colombeau algebra: generalized wave front sets and noncharacteristic regularity

Published: September 14, 2006
Keywords: Algebras of generalized functions, wave front sets, duality theory
Subject: 46F30, 35A18, 46A20, 35D10

We introduce different notions of wave front set for the functionals in the dual of the Colombeau algebra Gc(Ω) providing a way to measure the G and the G- regularity in L(Gc(Ω),\tilde{C}). For the smaller family of functionals having a "basic structure'' we obtain a Fourier transform-characterization for this type of generalized wave front sets and results of noncharacteristic G and G-regularity.


Supported by FWF (Austria), grant P16820-N04 and TWF (Tyrol), grant UNI-0404/305.

Author information

Institut für Technische Mathematik, Universität Innsbruck, Austria