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
SPECTRAL ANALYSIS OF NON-SELF-ADJOINT JACOBI OPERATOR ASSOCIATED WITH JACOBIAN ELLIPTIC FUNCTIONS
Stockholm University, Faculty of Science, Department of Mathematics. Universit├Ąt Bern, Switzerland.
Number of Authors: 2
2017 (English)In: Operators and Matrices, ISSN 1846-3886, E-ISSN 1848-9974, Vol. 11, no 4, 901-928 p.Article in journal (Refereed) Published
Abstract [en]

We perform the spectral analysis of a family of Jacobi operators J(alpha) depending on a complex parameter alpha. If |alpha| not equal 1 the spectrum of J(alpha) is discrete and formulas for eigenvalues and eigenvectors are established in terms of elliptic integrals and Jacobian elliptic functions. If |alpha| = 1, alpha not equal perpendicular to 1, the essential spectrum of J(alpha) covers the entire complex plane. In addition, a formula for theWeyl m-function as well as the asymptotic expansions of solutions of the difference equation corresponding to J(alpha) are obtained. Finally, the completeness of eigenvectors and Rodriguez-like formulas for orthogonal polynomials, studied previously by Carlitz, are proved.

Place, publisher, year, edition, pages
2017. Vol. 11, no 4, 901-928 p.
Keyword [en]
Non-self-adjoint Jacobi operator, Weyl m-function, Jacobian elliptic functions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-148820DOI: 10.7153/oam-2017-11-64ISI: 000413118300001OAI: oai:DiVA.org:su-148820DiVA: diva2:1156779
Available from: 2017-11-14 Created: 2017-11-14 Last updated: 2017-11-14Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Stampach, Frantisek
By organisation
Department of Mathematics
In the same journal
Operators and Matrices
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
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