Semiclassical hypoelliptic estimates with a big loss of derivatives
Alberto Parmeggiani, Karel Pravda-Starov
TL;DR
This paper investigates the spectral properties of pseudodifferential operators near critical points, establishing conditions for hypoelliptic estimates with significant derivative loss in a semiclassical setting.
Contribution
It provides necessary and sufficient conditions for semiclassical hypoelliptic estimates with large derivative loss for pseudodifferential operators around doubly characteristic points.
Findings
Characterization of pseudospectral properties near critical points
Necessary and sufficient conditions for hypoelliptic estimates with big loss
Insights into the behavior of pseudodifferential operators in semiclassical analysis
Abstract
We study the pseudospectral properties of general pseudodifferential operators around a doubly characteristic point and provide necessary and sufficient conditions for semiclassical hypoelliptic a priori estimates with a big loss of derivatives to hold.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNumerical methods in inverse problems · Advanced Mathematical Physics Problems · Spectral Theory in Mathematical Physics