RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2017, Volume 101, Issue 4, Pages 562–575 (Mi mz11246)  

On the Spectral Abscissa and the Logarithmic Norm

A. I. Perov, I. D. Kostrub

Voronezh State University

Abstract: In this paper, both well-known and new properties of the spectral abscissa and the logarithmic norm are described. In addition to well-known formulas for the norm of a matrix and for its logarithmic norm in cubic, octahedral, spherical norms, various estimates for these quantities in an arbitrary Hölder norm are proved.

Keywords: spectral radius and the norm of a matrix, spectral abscissa and the logarithmic norm of a matrix, Young's inequality, Hölder's inequality, Riesz theorem, Hölder norm.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00197
This work was supported by the Russian Foundation for Basic Research under grant 16-01-00197.


DOI: https://doi.org/10.4213/mzm11246

Full text: PDF file (506 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2017, 101:4, 677–687

Bibliographic databases:

UDC: 517.984
Received: 06.06.2016

Citation: A. I. Perov, I. D. Kostrub, “On the Spectral Abscissa and the Logarithmic Norm”, Mat. Zametki, 101:4 (2017), 562–575; Math. Notes, 101:4 (2017), 677–687

Citation in format AMSBIB
\Bibitem{PerKos17}
\by A.~I.~Perov, I.~D.~Kostrub
\paper On the Spectral Abscissa and the Logarithmic Norm
\jour Mat. Zametki
\yr 2017
\vol 101
\issue 4
\pages 562--575
\mathnet{http://mi.mathnet.ru/mz11246}
\crossref{https://doi.org/10.4213/mzm11246}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3629045}
\elib{http://elibrary.ru/item.asp?id=28931417}
\transl
\jour Math. Notes
\yr 2017
\vol 101
\issue 4
\pages 677--687
\crossref{https://doi.org/10.1134/S0001434617030257}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000401454600025}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85018846633}


Linking options:
  • http://mi.mathnet.ru/eng/mz11246
  • https://doi.org/10.4213/mzm11246
  • http://mi.mathnet.ru/eng/mz/v101/i4/p562

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:204
    References:37
    First page:32

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020