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

 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

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}