Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • 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
Multivariate Polya-Schur classification problems in the Weyl algebra
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-1055-1474
2010 (English)In: Proceedings of the London Mathematical Society, ISSN 0024-6115, E-ISSN 1460-244X, Vol. 101, 73-104 p.Article in journal (Refereed) Published
Abstract [en]

A multivariate polynomial is stable if it is nonvanishing whenever all variables have positive imaginary parts. We classify all linear partial differential operators in the Weyl algebra A(n) that preserve stability. An important tool that we develop in the process is the higher-dimensional generalization of Polya-Schur's notion of multiplier sequence. We characterize all multivariate multiplier sequences as well as those of finite order. Next, we establish a multivariate extension of the Cauchy-Poincare interlacing theorem and prove a natural analog of the Lax conjecture for real stable polynomials in two variables. Using the latter we describe all operators in A(1) that preserve univariate hyperbolic polynomials by means of determinants and homogenized symbols. Our methods also yield homotopical properties for symbols of linear stability preservers and a duality theorem showing that an operator in A(n) preserves stability if and only if its Fischer-Fock adjoint does. These are powerful multivariate extensions of the classical Hermite-Poulain-Jensen theorem, Polya's curve theorem and Schur-Malo-Szegocomposition theorems. Examples and applications to strict stability preservers are also discussed.

Place, publisher, year, edition, pages
2010. Vol. 101, 73-104 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-27229DOI: 10.1112/plms/pdp049ISI: 000279483800003Scopus ID: 2-s2.0-77956021403OAI: oai:DiVA.org:kth-27229DiVA: diva2:381872
Note
QC 20101229Available from: 2010-12-29 Created: 2010-12-09 Last updated: 2010-12-29Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Authority records BETA

Brändén, Petter

Search in DiVA

By author/editor
Brändén, Petter
By organisation
Mathematics (Dept.)
In the same journal
Proceedings of the London Mathematical Society
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 36 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • 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