The Discrete Spectrum in the Gaps of the Continuous One for Non-Signdefinite Perturbations with a Large Coupling Constant |
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Authors: | OL Safronov |
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Institution: | Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden.?E-mail: safronov@math.kth.se, SE
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Abstract: | Given two selfadjoint operators A and V=V
+ -V
-, we study the motion of the eigenvalues of the operator A(t)=A-tV as t increases. Let α>0 and let λ be a regular point for A. We consider the quantities N
+(λ,α), N
-(λ,α), N
0(λ,α) defined as the number of the eigenvalues of the operator A(t) that pass point λ from the right to the left, from the left to the right or change the direction of their motion exactly
at point λ, respectively, as t increases from 0 to α>0. An abstract theorem on the asymptotics for these quantities is presented. Applications to Schr?dinger
operators and its generalizations are given.
Received: 9 April 1997 / Accepted: 26 August 1997 |
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Keywords: | |
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