Abstract
We characterize the Hermite–Biehler (de Branges) functions E which correspond to Schroedinger operators with \(L^2\) potential on the finite interval. From this characterization one can easily deduce a recent theorem by Horvath. We also obtain a result about location of resonances.
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Acknowledgments
The authors are grateful to the referee for numerous helpful remarks and, especially, for suggesting a simplified proof of Statement 1 in Theorem 3.
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The work is supported by Russian Science Foundation Grant 14-41-00010.
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Baranov, A., Belov, Y. & Poltoratski, A. De Branges functions of Schroedinger equations. Collect. Math. 68, 251–263 (2017). https://doi.org/10.1007/s13348-016-0168-0
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DOI: https://doi.org/10.1007/s13348-016-0168-0