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

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

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
2. Gaishun I., “About One Scheme of Analysis of Unstability for Linear Functional-Differential Systems”, Dokl. Akad. Nauk Belarusi, 37:5 (1993), 5–8
3. Gaishun I., “Difference-Differential 2-Parameter Control-Systems”, Differ. Equ., 30:6 (1994), 861–867
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