Weak Bloch property for discrete magnetic Schrodinger operators

Nagoya Mathematical Journal

Volumn 161, Issue , 2001, Pages 127-154

  Higuchi, Yusuke ^a   Shirai, Tomoyuki ^b  

^a SHOWA UNIVERSITY   (Japan)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035294714     PISSN: 00277630     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0027763000022157     Document Type: Article

References (14)

1. R. Brooks, Combinatorial problems in spectral geometry, in the Proc. of Taniguchi Symp. "Curvature and topology of Riemannian manifolds" 1985, Lecture Note in Math., 1201 (1986), 14-32.
2. M. D. Choi, G. Elliott and N. Yui, Gauss polynomials and the rotation algebra, Invent. Math., 99 (1990), 225-246.
3. J. Dodziuk and L. Karp, Spectral and function theory for combinatorial Laplacians, Contemp. Math., 73 (1988), 25-40.
4. J. Dodziuk and W. S. Kendall, Combinatorial Laplacians and isoperimetric inequality, in "From local times to global geometry, control and physics" (K. D. Elworthy, ed.), Pitman Research Notes in Mathematics Series, 150 (1986), 68-74.
5. P. G. Harper, Single band motion of conduction electrons in a uniform magnetic field, Proc. Phys. Soc. London, A68 (1955), 874-878.
6. Yu. Higuchi, Boundary area growth and the spectrum of discrete Laplacian, preprint.
7. Yu. Higuchi and T. Shirai, The spectrum of magnetic Schrödinger operators on a graph with periodic structure, J. Funct. Anal., 169 (1999), 456-480.
8. _, A remark on the spectrum of magnetic Laplacian on a graph, Yokohama Math. J., 47 Special Issue (1999), 129-141.
9. D. R. Hofstadter, Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev., B14 (1976), 2239-2249.
10. T. Kobayashi, K. Ono and T. Sunada, Periodic Schrödinger operators on a manifold, Forum Math., 1 (1989), 69-79.
11. E. Lieb and M. Loss, Fluxes, Laplacians and Kasteleyn's theorem, Duke Math. J., 71 (1993), 337-363.
12. J. Milnor, A note on curvature and fundamental group, J. Differ. Geom., 2 (1968), 1-7.
13. M. C. Reed and B. Simon, Methods of Modern Mathematical Physics Vol. IV, Academic Press, New York, 1978.
14. T. Sunada, A discrete analogue of periodic magnetic Schrödinger operators, in "Geometry of the spectrum" (P. Parry, R. Brooks, C. Gordon, eds.), Contemporary Mathematics, 173 (1994), 283-299.