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

LUIS O. SILVA; GERALD TESCHL; JULIO H. TOLOZA

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

AMER MATHEMATICAL SOC

Lugar: Providence; Año: 2015 vol. 143 p. 2103 - 2115

0002-9939

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.