Article

**Proc. Amer. Math. Soc. 143, 2103-2115 (2015)**[DOI: 10.1090/S0002-9939-2014-12440-3]

## Singular Schrödinger operators as self-adjoint extensions of *N*-entire operators

### Luis O. Silva, Gerald Teschl, and Julio H. Toloza

We investigate the connections between Weyl-Titchmarsh-Kodaira
theory for one-dimensional Schrödinger operators and the theory of

*n*-entire operators. As our main result we find a necessary and sufficient condition for a one-dimensional Schrödinger 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.
** MSC2000:** Primary 34L40, 47B25; Secondary 46E22, 34B20

**Keywords:** *Schrödinger operators, de Branges spaces, Weyl-Titchmarsh-Kodaira theory*

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