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On polyharmonic operators with limit-periodic potential in dimension two
Author(s):
Yulia
Karpeshina;
Young-Ran
Lee
Journal:
Electron. Res. Announc. Amer. Math. Soc.
12
(2006),
113-120.
MSC (2000):
Primary 81Q15;
Secondary 81Q10
Posted:
August 11, 2006
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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 limit-periodic 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 high-energy region. Second, the isoenergetic curves in the space of momenta corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantor-type 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
Young-Ran
Lee
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
Email:
yrlee4@math.uiuc.edu
DOI:
10.1090/S1079-6762-06-00167-3
PII:
S 1079-6762(06)00167-3
Keywords:
Limit-periodic potential
Received by editor(s):
January 4, 2006
Posted:
August 11, 2006
Additional Notes:
Research partially supported by USNSF Grant DMS-0201383.
Dedicated:
In memory of our colleague and friend Robert M. Kauffman.
Communicated by:
Svetlana Katok
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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