Back to Search
Start Over
On resonances generated by conic diffraction
- Publication Year :
- 2017
-
Abstract
- We describe the resonances closest to the real axis generated by diffraction of waves among cone points on a manifold with Euclidean ends. These resonances lie asymptotically evenly spaced along a curve of the form $$\frac{\Im \lambda}{\log \left |\Re \lambda\right |}= -\nu;$$ here $\nu=(n-1)/2 L_0$ where $n$ is the dimension and $L_0$ is the length of the longest geodesic connecting two cone points. Moreover there are asymptotically no resonances below this curve and above the curve $$ \frac{\Im \lambda}{\log \left |\Re \lambda\right |}= -\Lambda $$ for a fixed $\Lambda>\nu.$<br />Comment: Slight correction to main theorem: finitely many different values of the constants $C_\Re$ and $C_\Im$ may be possible if there is more than one maximal diffracted closed orbit. Final version to appear in Ann. Inst. Fourier
- Subjects :
- Mathematics - Analysis of PDEs
Mathematical Physics
Mathematics - Spectral Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1706.07869
- Document Type :
- Working Paper