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

Direct link
Cite
Citation style
  • apa
  • 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
Biorthogonal Polynomials
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2017 (English)Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
Abstract [en]

In this thesis we present some fundamental results regarding orthogonal polynomials and biorthogonal polynomials, the latter defined as in the article "Cauchy Biorthogonal Polynomials", authored by Bertola, Gekhtman, and Szmigielski. We show that total positivity of the kernel can be weakened and how this implies that interlacement for biorthogonal polynomials holds in general. A counterexample is provided showing that in general there does not exist a four-term recurrence relation such as the one found for the Cauchy kernel. As a direct consequence we show that biorthogonal polynomial sequences cannot be considered orthogonal polynomial sequences by an appropriate choice of orthogonality measure. Furthermore, we motivate a conjecture stating that the more general form of interlacement that exists for orthogonal polynomials also exists for biorthogonal polynomials. We end with suggesting some further work that could be of interest.

Place, publisher, year, edition, pages
2017. , p. 79
Keywords [en]
Orthogonal polynomials, Biorthogonal polynomials, Totally positive kernel, Chebyshev system, Interlacement properties, Recurrence relations
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-140733ISRN: LiTH-MAT-EX--2017/15--SEOAI: oai:DiVA.org:liu-140733DiVA, id: diva2:1139867
Subject / course
Mathematics
Presentation
2017-08-31, Hopningspunkten, Campus Valla, Linköpings universitet, Linköping, 15:15 (English)
Supervisors
Examiners
Available from: 2017-09-11 Created: 2017-09-09 Last updated: 2017-09-11Bibliographically approved

Open Access in DiVA

Biorthogonal Polynomials(793 kB)189 downloads
File information
File name FULLTEXT01.pdfFile size 793 kBChecksum SHA-512
6d027f2f1e4765da5555e9b561688ffe97c4b2d3f9120aea532f390355cfda39af2863e28059a2c5cd5be08becd824fe831e5518d10434f72ebd815f064a6fb9
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Webb, Grayson
By organisation
Mathematics and Applied MathematicsFaculty of Science & Engineering
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 189 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

urn-nbn

Altmetric score

urn-nbn
Total: 569 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • 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