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Ufimsk. Mat. Zh., 2013, Volume 5, Issue 4, Pages 77–83 (Mi ufa223)  

On Bernstein inequality for vectors in Banach spaces

E. E. Dikarev

Voronezh State University, Voronezh, Russia

Abstract: We obtain the Bernstein inequality for the vectors in the Banach space of the isometric representation of a one-parametric group of the operators. We introduce the notion of an entire at infinity function. For such functions and for the norms of commutation operators we obtain the Bernstein inequality.

Keywords: Banach modulus, isometric representation, Beurling spectrum, entire function, commutation operator.

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English version:
Ufa Mathematical Journal, 2013, 5:4, 75–81 (PDF, 316 kB); https://doi.org/10.13108/2013-5-4-75

Document Type: Article
UDC: 517.9
MSC: 47A10, 47L10
Received: 21.09.2013

Citation: E. E. Dikarev, “On Bernstein inequality for vectors in Banach spaces”, Ufimsk. Mat. Zh., 5:4 (2013), 77–83; Ufa Math. J., 5:4 (2013), 75–81

Citation in format AMSBIB
\Bibitem{Dik13}
\by E.~E.~Dikarev
\paper On Bernstein inequality for vectors
in Banach spaces
\jour Ufimsk. Mat. Zh.
\yr 2013
\vol 5
\issue 4
\pages 77--83
\mathnet{http://mi.mathnet.ru/ufa223}
\elib{http://elibrary.ru/item.asp?id=20930478}
\transl
\jour Ufa Math. J.
\yr 2013
\vol 5
\issue 4
\pages 75--81
\crossref{https://doi.org/10.13108/2013-5-4-75}


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