Continuity of the scattering function and Levinson-type formula of Klein-Gordon equation (Q2857526)
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scientific article; zbMATH DE number 6222227
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Continuity of the scattering function and Levinson-type formula of Klein-Gordon equation |
scientific article; zbMATH DE number 6222227 |
Statements
Continuity of the scattering function and Levinson-type formula of Klein-Gordon equation (English)
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4 November 2013
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inverse problem on half line
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Gelfand-Levitan-Marchenko equation
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scattering function
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scattering data
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Levinson-type formula
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The paper deals with the scattering problem on the semi-line for the equation NEWLINE\[NEWLINEy''+(\lambda-q(x))^2 y =0,\quad x\in[0,\infty),NEWLINE\]NEWLINE with boundary conditions depending (in the form of second-order polynomials) on the spectral parameter. The equation can also be viewed as the Sturm-Liouville equation with energy dependent potential. Emphasis is made on proving the continuity of the reflection coefficient (scattering function) at \(\lambda=0\) and establishing the Levinson formula relating the number of zeros of the associated spectral function and the total change of the argument of the scattering function.
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