Topics in spectral and inverse spectral theory

This dissertation is concerned with two major classes of operators and provides various spectral and inverse spectral results for them. In the first part of this work a special class of one-dimensional discrete unitary operators is under investigation. The underlying Weyl-Titchmarsh theory and a Borg-type inverse spectral result are established for this class of operators. The second part of this work is devoted to some spectral theoretical questions for one- and multi-dimensional Schrödinger operators. In particular, the Weyl-Titchmarsh theory for one-dimensional self-adjoint Schrödinger operators with strongly singular potentials is established. In addition, a general perturbation theory for non-self-adjoint operators is developed and subsequently applied to a large class of non-self-adjoint multi-dimensional Schrödinger operators.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics (MU)

Grantor dc:publisher

University of Missouri--Columbia

Year dc:date.issued

2006

Author dc:creator

• Zinchenko, Maksym, 1980-

Advisor dc:contributor.advisor

• Gesztesy, Fritz, 1953-

Statement dc:rights

• OpenAccess.

Language dc:language.iso

eng, English

DOI

https://doi.org/10.32469/10355/4460

OAI identifier oai:identifier

oai:mospace.umsystem.edu:10355/4460