Subprincipal Control of Pseudospectral Quasimodes, II
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909987848060928 |
|---|---|
| author | Borgeke, Pelle Brook |
| author_facet | Borgeke, Pelle Brook |
| contents | In this paper, we continue the analysis of the effects of semiclassical sub principal controlled quasimodes, approximate solutions to P(h)u(h,b), depending on the subprincipal symbol b, which can give spectral insta bility (pseudospectrum). We consider a pseudodifferential operator, which has double zeros for the principal symbol, p. This means that p = dp = 0 in a small neighborhood. In the first paper in this series, we considered operators with transversal inter sections of bicharacteristics. Now we study operators with tangential in tersections of bicharacteristics, as well as with double characteristics for p. We put the pseudodifferential operator on normal form microlocally, and use a model operator, P(h) to test for quasimodes. We demonstrate two cases where this happens. We shall also continue with more advanced cases, when the operators are factorable to P(h) = P2(h)P1(h,B), thus annihilating the subprincipal control over the quasimodes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07743 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Subprincipal Control of Pseudospectral Quasimodes, II Borgeke, Pelle Brook Analysis of PDEs In this paper, we continue the analysis of the effects of semiclassical sub principal controlled quasimodes, approximate solutions to P(h)u(h,b), depending on the subprincipal symbol b, which can give spectral insta bility (pseudospectrum). We consider a pseudodifferential operator, which has double zeros for the principal symbol, p. This means that p = dp = 0 in a small neighborhood. In the first paper in this series, we considered operators with transversal inter sections of bicharacteristics. Now we study operators with tangential in tersections of bicharacteristics, as well as with double characteristics for p. We put the pseudodifferential operator on normal form microlocally, and use a model operator, P(h) to test for quasimodes. We demonstrate two cases where this happens. We shall also continue with more advanced cases, when the operators are factorable to P(h) = P2(h)P1(h,B), thus annihilating the subprincipal control over the quasimodes. |
| title | Subprincipal Control of Pseudospectral Quasimodes, II |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.07743 |