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Mathematics of the USSR-Sbornik, 1988, Volume 59, Issue 1, Pages 39–51
DOI: https://doi.org/10.1070/SM1988v059n01ABEH003123 (Mi sm1902) 		 
This article is cited in 5 scientific papers (total in 5 papers)

The geometry of the Hausdorff domain in localization problems for the spectrum of arbitrary matrices

A. A. Abdurakhmanov
English version PDF (599 kB) Citations (5)
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DOI: https://doi.org/10.1070/SM1988v059n01ABEH003123
Abstract: In this article it is shown that the Hausdorff domain (numerical range) $W(A)=\{(Ax,x):\|x\|=1\}$ is the union of the numerical ranges of a concretely constructed family of matrices acting in $\mathbf C^2$. In other words, a certain method of descent of the numerical range is justified. This method is used to study localizations for the spectra of arbitrary matrices. As a result, generalizations are discovered for results of Johnson, Gershgorin–Solov'ev, Hirsch and Bendixson, and Mees and Atherton.
Bibliography: 20 titles.
Received: 03.01.1985
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1986, Volume 131(173), Number 1(9), Pages 40–51
Bibliographic databases:
UDC: 512
MSC: Primary 15A18, 15A60; Secondary 34D05, 65F15
Language: English
Original paper language: Russian
Citation: A. A. Abdurakhmanov, “The geometry of the Hausdorff domain in localization problems for the spectrum of arbitrary matrices”, Mat. Sb. (N.S.), 131(173):1(9) (1986), 40–51; Math. USSR-Sb., 59:1 (1988), 39–51
Citation in format AMSBIB
\Bibitem{Abd86}
\by A.~A.~Abdurakhmanov
\paper The geometry of the Hausdorff domain in localization problems for the spectrum of arbitrary matrices
\jour Mat. Sb. (N.S.)
\yr 1986
\vol 131(173)
\issue 1(9)
\pages 40--51
\mathnet{http://mi.mathnet.ru/sm1902}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=868600}
\zmath{https://zbmath.org/?q=an:0646.47005|0621.47007}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 59
\issue 1
\pages 39--51
\crossref{https://doi.org/10.1070/SM1988v059n01ABEH003123}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:482
    Russian version PDF:138
    English version PDF:25
    References:65
     
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