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- W2793948280 abstract "The asymptotic and threshold behaviour of the eigenvalues of a perturbed difference operator inside a spectral gap is investigated. In particular, applications of the Titchmarsh-Weyl <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math>-function theory as well as the Birman-Schwinger principle is performed to investigate the existence and behaviour of the eigenvalues of the operator <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>0</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>λ</mml:mi><mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math> inside the spectral gap of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> in the limits <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mi>λ</mml:mi><mml:mo>↑</mml:mo><mml:mi mathvariant=normal>∞</mml:mi></mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mi>λ</mml:mi><mml:mo>↓</mml:mo><mml:mn mathvariant=normal>0</mml:mn><mml:mo>.</mml:mo></mml:math>" @default.
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- W2793948280 date "2018-01-01" @default.
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- W2793948280 title "A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic Potential" @default.
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- W2793948280 doi "https://doi.org/10.1155/2018/4696790" @default.
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