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Mat. Sb. (N.S.), 1978, Volume 105(147), Number 2, Pages 269–285 (Mi msb2529)  

This article is cited in 3 scientific papers (total in 3 papers)

Estimates of the spectra and the invertibility of functional operators

V. E. Slyusarchuk


Abstract: For an $\mathfrak R$-valued function $f(z_1,…,z_n)$ ($\mathfrak R$ is a Banach algebra) that is holomorphic in a neighborhood $\Omega$ of the joint spectrum of $n$ elements $B_1,…,B_n\in\mathfrak R$ that commute with each other and with $f(z_1,…,z_n)$ $\forallż=(z_1,…,z_n)\in\Omega$, the function $f(B_1,…,B_n)$ is introduced and estimates of the spectrum $\sigma(f(B_1,…,B_n))$ are given, one of which generalizes the maximum principle for holomorphic functions. The estimates of $\sigma(f(B_1,…,B_n))$ are used to solve problems on the invertibility of transformers, operators induced by discrete systems and operators induced by linear differential equations with constant deviations of the argument.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1978, 34:2, 243–258

Bibliographic databases:

UDC: 517.948.35+517.949.22
MSC: 47A10, 47A60
Received: 26.01.1977

Citation: V. E. Slyusarchuk, “Estimates of the spectra and the invertibility of functional operators”, Mat. Sb. (N.S.), 105(147):2 (1978), 269–285; Math. USSR-Sb., 34:2 (1978), 243–258

Citation in format AMSBIB
\Bibitem{Sly78}
\by V.~E.~Slyusarchuk
\paper Estimates of the spectra and the invertibility of functional operators
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 105(147)
\issue 2
\pages 269--285
\mathnet{http://mi.mathnet.ru/msb2529}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=512720}
\zmath{https://zbmath.org/?q=an:0377.47005|0403.47004}
\transl
\jour Math. USSR-Sb.
\yr 1978
\vol 34
\issue 2
\pages 243--258
\crossref{https://doi.org/10.1070/SM1978v034n02ABEH001159}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. E. Slyusarchuk, “Invertibility of almost periodic $c$-continuous functional operators”, Math. USSR-Sb., 44:4 (1983), 431–446  mathnet  crossref  mathscinet  zmath
    2. Gaishun I., “About One Scheme of Analysis of Unstability for Linear Functional-Differential Systems”, Dokl. Akad. Nauk Belarusi, 37:5 (1993), 5–8  mathscinet  zmath  isi
    3. Gaishun I., “Difference-Differential 2-Parameter Control-Systems”, Differ. Equ., 30:6 (1994), 861–867  mathnet  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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