On polyharmonic operators with limitperiodic potential in dimension two
Authors:
Yulia Karpeshina and YoungRan Lee
Journal:
Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 113120
MSC (2000):
Primary 81Q15; Secondary 81Q10
Published electronically:
August 11, 2006
MathSciNet review:
2237275
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Abstract: This is an announcement of the following results. We consider a polyharmonic operator in dimension two with and being a limitperiodic potential. We prove that the spectrum of contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves at the highenergy region. Second, the isoenergetic curves in the space of momenta corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantortype structure). Third, the spectrum corresponding to the eigenfunctions (the semiaxis) is absolutely continuous.
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Additional Information
Yulia Karpeshina
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, 1300 University Boulevard, Birmingham, Alabama 35294
Email:
karpeshi@math.uab.edu
YoungRan Lee
Affiliation:
Department of Mathematics, University of Illinois at UrbanaChampaign, 1409 W. Green Street, Urbana, Illinois 61801
Email:
yrlee4@math.uiuc.edu
DOI:
http://dx.doi.org/10.1090/S1079676206001673
PII:
S 10796762(06)001673
Keywords:
Limitperiodic potential
Received by editor(s):
January 4, 2006
Published electronically:
August 11, 2006
Additional Notes:
Research partially supported by USNSF Grant DMS0201383.
Dedicated:
In memory of our colleague and friend Robert M. Kauffman.
Communicated by:
Svetlana Katok
Article copyright:
© Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
