The uniqueness of the integrated density of states for the Schrödinger operators with magnetic fields

被引：0
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作者：
Shin-ichi Doi
Akira Iwatsuka
Takuya Mine
机构：
[1] Institute of Mathematics,
[2] University of Tsukuba,undefined
[3] Tsukuba 305-8571,undefined
[4] Japan (e-mail: doi@math.tsukuba.ac.jp) ,undefined
[5] Kyoto Institute of Technology,undefined
[6] Sakyo-ku,undefined
[7] Kyoto 606-8585,undefined
[8] Japan (e-mail: iwatsuka@ipc.kit.ac.jp) ,undefined
[9] Department of Mathematics,undefined
[10] Faculty of Science,undefined
[11] Kyoto University,undefined
[12] Sakyo-ku,undefined
[13] Kyoto 606-8502,undefined
[14] Japan (e-mail: mine@kusm.kyoto-u.ac.jp) ,undefined
来源：
Mathematische Zeitschrift | 2001年 / 237卷
关键词：
Boundary Condition; Magnetic Field; Functional Analysis; Space Operator; Dirichlet Boundary;
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摘要：
The integrated density of states (IDS) for the Schrödinger operators is defined in two ways: by using the counting function of eigenvalues of the operator restricted to bounded regions with appropriate boundary conditions or by using the spectral projection of the whole space operator. A sufficient condition for the coincidence of the two definitions above is given. Moreover, a sufficient condition for the coincidence of the IDS for the Dirichlet boundary conditions and the IDS for the Neumann boundary conditions is given. The proof is based only on the fundamental items in functional analysis, such as the min-max principle, etc.
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页码：335 / 371
页数：36
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