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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