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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Volume 17, Number 3, Pages 186–200 (Mi timm731)  
This article is cited in 5 scientific papers (total in 5 papers)

Some classes of functions of a linear closed operator

L. F. Korkina, M. A. Rekant

Ural Federal University
Full-text PDF (209 kB) Citations (5)
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Abstract: A linear closed densely defined operator and some domain $\Omega$ lying in the regular set of the operator and containing the negative real semiaxis of the real line are specified in a Banach space. We assume that power estimates for the norm of the resolvent operator are known at zero and infinity. We use the Cauchy integral formula to introduce operator functions generated by scalar functions that are analytic in a certain domain not containing the origin and containing the complement of $\Omega$ and have power estimates for their absolute values at zero and infinity. We study some properties of operator functions, which were studied by the authors earlier for the case of an operator whose inverse operator is bounded; in particular, we study the multiplicative property.
Keywords: linear closed operator, functions of an operator, multiplicative property, invertibility.
Received: 17.10.2010
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2012, Volume 277, Issue 1, Pages 121–135
DOI: https://doi.org/10.1134/S0081543812050124
Bibliographic databases:
Document Type: Article
UDC: 517.983.23
Language: Russian
Citation: L. F. Korkina, M. A. Rekant, “Some classes of functions of a linear closed operator”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 3, 2011, 186–200; Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 121–135
Citation in format AMSBIB
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\paper Some classes of functions of a~linear closed operator
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\vol 17
\issue 3
\pages 186--200
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2012
\vol 277
\issue , suppl. 1
\pages 121--135
\crossref{https://doi.org/10.1134/S0081543812050124}
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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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