Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Generalized Titchmarsh-Weyl functions and super singular perturbations
Stockholm University, Faculty of Science, Department of Mathematics.
2015 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

In this thesis we study certain singular Sturm-Liouville differential expressions from an operator theoretic point of view.In particular we are interested in expressions that involve strongly singular potentials as introduced by Gesztesy and Zinchenko.On the ODE side, analyzing these expressions involves the so-called $m$-functions, often generalized Nevanlinna functions, who encapsulate spectral information of the underlying problem.The aim of the two papers in this thesis is to further understanding on the operator theory side.In the first paper, we use a model for super singular perturbations to describe a family of induced self-adjoint realizations of a perturbed Schr\"o\-din\-ger operator, i.e., with a potential of the form $c/x^2 + q$ where $q$ is a perturbation.Following the unperturbed example of Kurasov and Luger, we find that the so-called $Q$-function appearing in this approach is in good agreement with the above named $m$-function.Furthermore, we show that the operator model can be chosen such that $Q \equiv m$.In the second paper, we present a negative result in this area, namely that the supersingular perturbations model cannot be used for all strongly singular potentials.For a potential with a stronger singularity at the origin, namely $1/x^4$, we discuss the asymptotic behaviour of the Weyl solution at zero.It turns out that this function cannot be regularized appropriately and the operator model breaks down.

Place, publisher, year, edition, pages
Stockholm: Stockholm University, 2015. , 74 p.
Keyword [en]
Generalized Titchmarsh-Weyl function, Super singular perturbations, Strongly singular potentials
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:su:diva-113389ISBN: 978-91-7649-075-4 (print)OAI: oai:DiVA.org:su-113389DiVA: diva2:784627
Presentation
2015-02-20, 306, Kräftriket, hus 6, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2015-02-03 Created: 2015-01-29 Last updated: 2015-02-03Bibliographically approved

Open Access in DiVA

fulltext(362 kB)147 downloads
File information
File name FULLTEXT01.pdfFile size 362 kBChecksum SHA-512
d6936ced80f6981c472958bc95d76d81f34f504ff8351f1551920a64bc025554979c0ae162a130c268a093bc87fe769753137b714682ae98a871e24e9f7b94cc
Type fulltextMimetype application/pdf

By organisation
Department of Mathematics
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar
Total: 147 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 218 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf