liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • 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
Hardy-Carleman type inequalities for Dirac operators
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2015 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 10, p. 103503-Article in journal (Refereed) Published
Abstract [en]

General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities is established. The case of a Dirac particle in a (potential) magnetic field is also considered. The methods used are direct and based on quadratic form techniques. (C) 2015 AIP Publishing LLC.

Place, publisher, year, edition, pages
AMER INST PHYSICS , 2015. Vol. 56, no 10, p. 103503-
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-123075DOI: 10.1063/1.4933241ISI: 000364237000030OAI: oai:DiVA.org:liu-123075DiVA, id: diva2:876573
Available from: 2015-12-04 Created: 2015-12-03 Last updated: 2018-02-13
In thesis
1. Resolvent Estimates and Bounds on Eigenvalues for Schrödinger and Dirac Operators
Open this publication in new window or tab >>Resolvent Estimates and Bounds on Eigenvalues for Schrödinger and Dirac Operators
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns the spectral theory of Schrödinger and Dirac operators. The main results relate to the problems of estimating perturbed eigenvalues. The thesis is based on four papers.

The first paper focuses on the problem of localization of perturbed eigenvalues for multidimensional Schrödinger operators. Bounds for eigenvalues, lying outside the essential spectrum, are obtained in terms of the Lebesgue's classes. The methods used make it possible to consider the general case of non-self-adjoint operators, and involve the weak Lebesgue's potentials. The results are extended to the case of the polyharmonic operators.

In the second paper, the problem of location of the discrete spectrum is solved for the class of Schrödinger operators considered on the half-line. The general case of complex-valued potentials, imposing various boundary conditions, typically Dirichlet and Neumann conditions, is considered. General mixed boundary conditions are also treated.

The third paper is devoted to Dirac operators. The case of spherically symmetric potentials is considered. Estimates for the eigenvalues are derived from the asymptotic behaviour of the resolvent of the free Dirac operator. For the massless Dirac operators, whose essential spectrum is the whole real line, optimal bounds for the imaginary part of the eigenvalues are established.

In the fourth paper, new Hardy-Carleman type inequalities for Dirac operators are proven. Concrete Carleman type inequalities, useful in applications, Agmon and also Treve type inequalities are derived from the general results by involving special weight functions. The results are extended to the case of the Dirac operator describing the relativistic particle in a potential magnetic field.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 39
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1906
Keyword
Spectral theory, Schrödinger operators, polyharmonic operators, Dirac operators, non-self-adjoint perturbations, complex potential, estimation of eigenvalues, Carleman inequalities, Hardy inequalities
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-145173 (URN)10.3384/diss.diva-145173 (DOI)9789176853627 (ISBN)
Public defence
2018-03-28, BL32, B-huset, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2018-02-14 Created: 2018-02-13 Last updated: 2018-05-17Bibliographically approved

Open Access in DiVA

fulltext(249 kB)79 downloads
File information
File name FULLTEXT01.pdfFile size 249 kBChecksum SHA-512
e36db1224ba220899d84dbfd5b44be5e6ac33d861ce812b43fc11df625f74cd8b1e29866f2c8b8e730e668f4f6bd66c3fe980d11c88e1e8538ce778be576ea3b
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Authority records BETA

Enblom, Alexandra

Search in DiVA

By author/editor
Enblom, Alexandra
By organisation
Mathematics and Applied MathematicsFaculty of Science & Engineering
In the same journal
Journal of Mathematical Physics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 79 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

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 164 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • 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