Journal d’Analyse Mathématique

, Volume 75, Issue 1, pp 51–66

Microlocal analysis of Colombeau’s generalized functions: Propagation of singularities

Article

DOI: 10.1007/BF02788691

Cite this article as:
Dapić, N., Pilipović, S. & Scarpalézos, D. J. Anal. Math. (1998) 75: 51. doi:10.1007/BF02788691

Abstract

We introduce the notion of pointwise regularity (\(\dot {\mathcal{G}}^\infty \)) of Colombeau’s generalized functions and give comparison theorems between\(\dot {\mathcal{G}}^\infty \) regularity,\(\mathcal{G}^\infty \)- andC-regularity. We also define the notion of a pointwise wave front set and establish a theorem concerning the effect of a linear generalized partial differential operator on such a wave front.

Copyright information

© Hebrew University of Jerusalem 1998

Authors and Affiliations

  1. 1.Faculty of Science Institute for MathematicsUniversity of Novi SadNovi SadYugoslavia
  2. 2.U. F. R. de MathématiquesUniversité Paris 7ParisFrance