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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 434, Pages 5–18
(Mi znsl6137)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/znsl6137 https://www.mathnet.ru/eng/znsl/v434/p5
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