TY - JOUR
T1 - The Spectrum of Magnetic Schrödinger Operators on a Graph with Periodic Structure
AU - Higuchi, Yusuke
AU - Shirai, Tomoyuki
N1 - Funding Information:
This work was supported in part by the Ministry of Education, Science, Sports and Culture of Japan under the Grant-in-Aid No. 09304022 (first author) and No. 70302932 (second author).
PY - 1999/12/20
Y1 - 1999/12/20
N2 - For discrete magnetic Schrödinger operators on covering graphs of a finite graph, we investigate two spectral properties: (1) the relationship between the spectrum of the operator on the covering graph and that on a finite graph, (2) the analyticity of the bottom of the spectrum with respect to magnetic flow. Also we compute the second derivative of the bottom of the spectrum and represent it in terms of geometry of a graph.
AB - For discrete magnetic Schrödinger operators on covering graphs of a finite graph, we investigate two spectral properties: (1) the relationship between the spectrum of the operator on the covering graph and that on a finite graph, (2) the analyticity of the bottom of the spectrum with respect to magnetic flow. Also we compute the second derivative of the bottom of the spectrum and represent it in terms of geometry of a graph.
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U2 - 10.1006/jfan.1999.3478
DO - 10.1006/jfan.1999.3478
M3 - Article
AN - SCOPUS:0007543801
SN - 0022-1236
VL - 169
SP - 456
EP - 480
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -