Formulas of Szegő Type for the Periodic Schrödinger Operator

Formulas of Szegő Type for the Periodic Schrödinger Operator We prove asymptotic formulas of Szegő type for the periodic Schrödinger operator $${H = -\frac{d^2}{dx^2}+V}$$ H = - d 2 d x 2 + V in dimension one. Admitting fairly general functions h with $${h(0)=0}$$ h ( 0 ) = 0 , we study the trace of the operator $${h(\chi_{(-\alpha,\alpha)} \chi_{(-\infty,\mu)}(H)\chi_{(-\alpha,\alpha)})}$$ h ( χ ( - α , α ) χ ( - ∞ , μ ) ( H ) χ ( - α , α ) ) and link its subleading behaviour as $${\alpha \to \infty}$$ α → ∞ to the position of the spectral parameter μ relative to the spectrum of H. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematical Physics Springer Journals

Formulas of Szegő Type for the Periodic Schrödinger Operator

Loading next page...
 
/lp/springer_journal/formulas-of-szeg-type-for-the-periodic-schr-dinger-operator-MnSn1JiMJD
Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by The Author(s)
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory
ISSN
0010-3616
eISSN
1432-0916
D.O.I.
10.1007/s00220-018-3106-z
Publisher site
See Article on Publisher Site

Abstract

We prove asymptotic formulas of Szegő type for the periodic Schrödinger operator $${H = -\frac{d^2}{dx^2}+V}$$ H = - d 2 d x 2 + V in dimension one. Admitting fairly general functions h with $${h(0)=0}$$ h ( 0 ) = 0 , we study the trace of the operator $${h(\chi_{(-\alpha,\alpha)} \chi_{(-\infty,\mu)}(H)\chi_{(-\alpha,\alpha)})}$$ h ( χ ( - α , α ) χ ( - ∞ , μ ) ( H ) χ ( - α , α ) ) and link its subleading behaviour as $${\alpha \to \infty}$$ α → ∞ to the position of the spectral parameter μ relative to the spectrum of H.

Journal

Communications in Mathematical PhysicsSpringer Journals

Published: Mar 6, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial