By relating the problem to the study of the number of zeros of certain wronskian determinants, estimates are found for the number of zeros on the real line of functions of a certain class. This class is instanced by functions of the shape m Z Pt(@ exp Qd-4 k=l where the Pa, QI~ are polynomials and t
Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function
✍ Scribed by Helge Krüger; Gerald Teschl
- Publisher
- Springer
- Year
- 2008
- Tongue
- English
- Weight
- 361 KB
- Volume
- 287
- Category
- Article
- ISSN
- 0010-3616
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract We consider the three‐dimensional Schrödinger operator with constant magnetic field of strength __b__ > 0, and with smooth electric potential. The weak asymptotics of the spectral shift function with respect to __b__ ↗ +∞ is studied. First, we fix the distance to the Landau levels, then
It is well known that the sum of negative (positive) eigenvalues of some finite Hermitian matrix V is concave (convex) with respect to V. Using the theory of the spectral shift function we generalize this property to self-adjoint operators on a separable Hilbert space with an arbitrary spectrum. Mor