In this article, we define a generalisation ofmicrolocal defectmeasures (also known as H-measures) to the setting of graded nilpotent Lie groups. This requires to develop the notions of homogeneous symbols and classical pseudodifferential calculus adapted to this setting and defined via the representations of the groups. Our method relies on the study of the C*-algebra of 0-homogeneous symbols. Then, we compute microlocal defect measures for concentrating and oscillating sequences, which also requires to investigate the notion of oscillating sequences in graded Lie groups. Finally, we discuss compensated compactness approaches in the context of graded nilpotent Lie groups.
|Number of pages||85|
|Journal||Annali della Scuola Normale Superiore di Pisa - Classe di Scienze|
|Publication status||Published - 22 Dec 2020|
ASJC Scopus subject areas
- Theoretical Computer Science
- Mathematics (miscellaneous)