Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials
Publication
, Journal Article
Kim, A; Kiselev, A
Published in: Mathematische Nachrichten
April 1, 2009
We show that when a potential bn of a discrete Schrödinger operator, defined on l2(Z{double-struck}+), slowly oscillates satisfying the conditions bn ∈ l∞ and ∂bn = bn+1 - bn ∈ lp, p < 2, then all solutions of the equation Ju = Eu are bounded near infinity at almost every E ∈ [-2 + lim supn→∞ bn, 2 + lim supn→∞ bn] ∩ [-2 + lim infn→∞bn, 2 + lim infn→∞bn]. We derive an asymptotic formula for generalized eigenfunctions in this case. As a corollary, the absolutely continuous spectrum of the corresponding Jacobi operator is essentially supported on the same interval of E. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Duke Scholars
Published In
Mathematische Nachrichten
DOI
EISSN
1522-2616
ISSN
0025-584X
Publication Date
April 1, 2009
Volume
282
Issue
4
Start / End Page
552 / 568
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Kim, A., & Kiselev, A. (2009). Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials. Mathematische Nachrichten, 282(4), 552–568. https://doi.org/10.1002/mana.200810754
Kim, A., and A. Kiselev. “Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials.” Mathematische Nachrichten 282, no. 4 (April 1, 2009): 552–68. https://doi.org/10.1002/mana.200810754.
Kim A, Kiselev A. Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials. Mathematische Nachrichten. 2009 Apr 1;282(4):552–68.
Kim, A., and A. Kiselev. “Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials.” Mathematische Nachrichten, vol. 282, no. 4, Apr. 2009, pp. 552–68. Scopus, doi:10.1002/mana.200810754.
Kim A, Kiselev A. Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials. Mathematische Nachrichten. 2009 Apr 1;282(4):552–568.
Published In
Mathematische Nachrichten
DOI
EISSN
1522-2616
ISSN
0025-584X
Publication Date
April 1, 2009
Volume
282
Issue
4
Start / End Page
552 / 568
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics