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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 434, Pages 5–18 (Mi znsl6137)  

This article is cited in 2 scientific papers (total in 2 papers)

Commutator Lipschitz functions and analytic continuation

A. B. Aleksandrov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (231 kB) Citations (2)
References:
Abstract: Let $\mathfrak F_0$ and $\mathfrak F$ be perfect subsets of the complex plane $\mathbb C$. Assume that $\mathfrak{F_0\subset F}$ and the set $\Omega\stackrel{\mathrm{def}}=\mathfrak{F\setminus F}_0$ is open. We say that a continuous function $f\colon\mathfrak F\to\mathbb C$ is an analytic continuation of the function $f_0\colon\mathfrak F_0\to\mathbb C$ if $f$ is analytic on $\Omega$ and $f|\mathfrak F_0=f_0$. In the paper it is proved that if $\mathfrak F$ is bounded, then the commutator Lipschitz seminorm of the analytic continuation $f$ coincides with the commutator Lipschitz seminorm of $f_0$. The same is true for unbounded $\mathfrak F$ if some natural restrictions concerning the behavior of $f$ at infinity are imposed.
Key words and phrases: operator Lipschitz functions.
Received: 05.05.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 215, Issue 5, Pages 543–551
DOI: https://doi.org/10.1007/s10958-016-2859-1
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: A. B. Aleksandrov, “Commutator Lipschitz functions and analytic continuation”, Investigations on linear operators and function theory. Part 43, Zap. Nauchn. Sem. POMI, 434, POMI, St. Petersburg, 2015, 5–18; J. Math. Sci. (N. Y.), 215:5 (2016), 543–551
Citation in format AMSBIB
\Bibitem{Ale15}
\by A.~B.~Aleksandrov
\paper Commutator Lipschitz functions and analytic
continuation
\inbook Investigations on linear operators and function theory. Part~43
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 434
\pages 5--18
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6137}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3493695}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 215
\issue 5
\pages 543--551
\crossref{https://doi.org/10.1007/s10958-016-2859-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84965066396}
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  • https://www.mathnet.ru/eng/znsl/v434/p5
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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