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arXiv · 1310.6308

Singular Schroedinger operators as self-adjoint extensions of n-entire operators

Luis O. Silva·Gerald Teschl·Julio H. Toloza
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Abstract

We investigate the connections between Weyl-Titchmarsh-Kodaira theory for one-dimensional Schr\"odinger operators and the theory of $n$-entire operators. As our main result we find a necessary and sufficient condition for a one-dimensional Schr\"odinger operator to be $n$-entire in terms of square integrability of derivatives (w.r.t. the spectral parameter) of the Weyl solution. We also show that this is equivalent to the Weyl function being in a generalized Herglotz-Nevanlinna class. As an application we show that perturbed Bessel operators are $n$-entire, improving the previously known conditions on the perturbation.

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Luis O. Silva, Gerald Teschl, Julio H. Toloza. 2013-10-23. Singular Schroedinger operators as self-adjoint extensions of n-entire operators. https://doi.org/10.1090/s0002-9939-2014-12440-3

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