Uniform convergence of spectral shift functions

Physics – Mathematical Physics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

For the procceedings of the RIMS workshop "Spectra of Random Operators and Related Topics" in Kyoto, December 2009

Scientific paper

The spectral shift function \xi_{L}(E) for a Schr\"odinger operator restricted to a finite cube of length L in multi-dimensional Euclidean space, with Dirichlet boundary conditions, counts the number of eigenvalues less than or equal to E \in \RR created by a perturbation potential V. We study the behavior of this function \xi_{L}(E) as L to infinity for the case of a compactly-supported and bounded potential V. After reviewing results of Kirsch [Proc. Amer. Math. Soc. 101, 509-512 (1987)], and our recent pointwise convergence result for the Ces\`aro mean [Proc. Amer. Math. Soc. 138, 2141-2150 (2010)], we present a new result on the convergence of the energy-averaged spectral shift function that is uniform with respect to the location of the potential V within the finite box.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Uniform convergence of spectral shift functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Uniform convergence of spectral shift functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniform convergence of spectral shift functions will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-50368

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.