摘要 :
We consider the problem of reconstructing an even polynomial potential from one set of spectral data of a Sturm-Liouville problem. We show that we can recover an even polynomial of degree 2m from m + 1 given Taylor coefficients of...
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We consider the problem of reconstructing an even polynomial potential from one set of spectral data of a Sturm-Liouville problem. We show that we can recover an even polynomial of degree 2m from m + 1 given Taylor coefficients of the characteristic function whose zeros are the eigenvalues of one spectrum. The idea here is to represent the solution as a power series and identify the unknown coefficients from the characteristic function. We then compute these coefficients by solving a nonlinear algebraic system, and provide numerical examples at the end. Because of its algebraic nature, the method applies also to non self-adjoint problems.
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摘要 :
In this paper we derive a trace formula for the Schrodinger operator on the half-line. As a consequence we obtain a Schmincke type inequality with sharp constant. The main tool in our investigation is the inverse spectral Gelfand-...
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In this paper we derive a trace formula for the Schrodinger operator on the half-line. As a consequence we obtain a Schmincke type inequality with sharp constant. The main tool in our investigation is the inverse spectral Gelfand-Levitan theory, which allows us to compare two Schrodinger operators whose spectra differ by few eigenvalues.
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