𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Weak asymptotics of the spectral shift function

✍ Scribed by Vincent Bruneau; Mouez Dimassi

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
194 KB
Volume
280
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We consider the three‐dimensional SchrΓΆdinger 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 β†— +∞ is studied. First, we fix the distance to the Landau levels, then the distance to Landau levels tends to infinity as b β†— +∞. In particular we give explicitly the leading terms in the asymptotics and in some case we obtain full asymptotics expansions. (Β© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

πŸ“œ SIMILAR VOLUMES

The Spectral Shift Function and the Inva
The Spectral Shift Function and the Invariance Principle
✍ Alexander Pushnitski πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 308 KB

The new representation formula for the spectral shift function due to F. Gesztesy and K. A. Makarov is considered. This formula is extended to the case of relatively trace class perturbations. The proof is based on the analysis of a certain new unitary invariant for a pair of self-adjoint operators.

Concavity of Eigenvalue Sums and the Spe
Concavity of Eigenvalue Sums and the Spectral Shift Function
✍ Vadim Kostrykin πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 170 KB

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

Asymptotics of the hypergeometric functi
Asymptotics of the hypergeometric function
✍ D. S. Jones πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 159 KB

## Abstract An asymptotic representation is obtained for the hypergeometric function ${\bf F}(a+\lambda,b‐\lambda,c,1/2‐1/2z)$\nopagenumbers\end as $|\lambda|\rightarrow\infty$\nopagenumbers\end with $|{\rm ph}\,\lambda|<\pi$\nopagenumbers\end. It is uniformly valid in the __z__‐plane cut in an app

Spectral Shift Function in the Large Cou
Spectral Shift Function in the Large Coupling Constant Limit
✍ O Safronov πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 148 KB

Given two selfadjoint operators H 0 and V=V + &V & , we study the spectrum of the operator H(:)=H 0 +:V, :>0. We consider the quantity !(\*, H(:), H 0 ), \* # R, which coincides with Krein's spectral shift function of the pair H(:), H 0 if V is of trace class and study its asymptotic behavior as : Γ„

Asymptotic Behaviour of Spectral Functio
Asymptotic Behaviour of Spectral Functions and Singularities of Wightman Functions and Field Commutators
✍ Prof. Dr. F. Kaschluhn; Dr. E. Wieczorek πŸ“‚ Article πŸ“… 1971 πŸ› John Wiley and Sons 🌐 English βš– 166 KB

Singulartics of WICHTJIAK functions and field commutators are studied in localizable and nonlocalizable cases including the spectral behaviour u(@) = exp (a@), 01 > 0. Some results are discussed concerning polynomially as well as exponentially increasing spectral functions and the corresponding sin