Back to Search
Start Over
Bounds for Eigenvalue Sums of Schr\'odinger Operators with Complex Radial Potentials
- Publication Year :
- 2024
-
Abstract
- We consider eigenvalue sums of Schr\"odinger operators $-\Delta+V$ on $L^2(\R^d)$ with complex radial potentials $V\in L^q(\R^d)$, $q<d$. We prove quantitative bounds on the distribution of the eigenvlaues in terms of the $L^q$ norm of $V$. A consequence of our bounds is that, if the eigenvlaues $(z_j)$ accumulates to a point in $(0,\infty)$, then $(\im z_j)$ is summable. The key technical tools are resolvent estimates in Schatten spaces. We show that these resolvent estimates follow from spectral measure estimates by an epsilon removal argument.<br />Comment: Minor misprints corrected
- Subjects :
- Mathematics - Spectral Theory
Mathematical Physics
Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.15783
- Document Type :
- Working Paper