We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Regularity, Local and Microlocal Analysis in Theories of Generalized Functions.
- Authors
Marti, Jean-André
- Abstract
We introduce a general context involving a presheaf $\mathcal{A}$ and a subpresheaf ℬ of $\mathcal{A}$ . We show that all previously considered cases of local analysis of generalized functions (defined from duality or algebraic techniques) can be interpretated as the ℬ-local analysis of sections of $\mathcal{A}$ . But the microlocal analysis of the sections of sheaves or presheaves under consideration is dissociated into a “frequential microlocal analysis” and into a “microlocal asymptotic analysis”. The frequential microlocal analysis based on the Fourier transform leads to the study of propagation of singularities under only linear (including pseudodifferential) operators in the theories described here, but has been extended to some non linear cases in classical theories involving Sobolev techniques. The microlocal asymptotic analysis is a new spectral study of singularities. It can inherit from the algebraic structure of ℬ some good properties with respect to nonlinear operations.
- Subjects
SHEAF theory; MICROLOCAL analysis; THEORY of distributions (Functional analysis); LOCALIZATION theory; FOURIER transforms; SPECTRAL geometry; NONLINEAR partial differential operators
- Publication
Acta Applicandae Mathematicae, 2009, Vol 105, Issue 3, p267
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-008-9275-6