Singular Schrödinger operators as self-adjoint extensions of $N$-entire operators
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- by Luis O. Silva, Gerald Teschl and Julio H. Toloza PDF
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Abstract:
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.References
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Additional Information
- Luis O. Silva
- Affiliation: Departamento de Física Matemática, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, C.P. 04510, México D.F.
- Email: silva@iimas.unam.mx
- Gerald Teschl
- Affiliation: Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria — and — International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria
- Email: Gerald.Teschl@univie.ac.at
- Julio H. Toloza
- Affiliation: CONICET — and — Centro de Investigación en Informática para la Ingeniería, Universidad Tecnológica Nacional – Facultad Regional Córdoba, Maestro López s/n, X5016ZAA Córdoba, Argentina
- Email: jtoloza@scdt.frc.utn.edu.ar
- Received by editor(s): October 23, 2013
- Published electronically: December 18, 2014
- Additional Notes: The authors’ research was supported by the Austrian Science Fund (FWF) under Grant No. Y330 and by CONICET (Argentina) through grant PIP 112-201101-00245
- Communicated by: Joachim Krieger
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 2103-2115
- MSC (2010): Primary 34L40, 47B25; Secondary 46E22, 34B20
- DOI: https://doi.org/10.1090/S0002-9939-2014-12440-3
- MathSciNet review: 3314119