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 Mat. Zametki, 2004, Volume 75, Issue 2, Pages 253–260 (Mi mz31)

This article is cited in 1 scientific paper (total in 1 paper)

Existence Theorems for Momentum Representations Generalized in the Sense of Dzyadyk

G. V. Radzievskii

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: In this paper, in particular, we prove that, for any sequence of complex numbers $\{c_n\}_{n=0}^\infty$, there exists a closed linear operator $A$ acting in the Hilbert space and two vectors $x$ and $y$ lying in the domains of definition of all powers of the operator $A$ for which the relation $c_n=(A^n x, y)$ holds. But if the series $\sum_{n=0}^\infty c_n z^n$ has radius of convergence $R > 0$, then in the representation $c_n=(A^nx,y)$, the operator $A$ can be chosen to be bounded with a spectral radius equal to $1/R$.

DOI: https://doi.org/10.4213/mzm31

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English version:
Mathematical Notes, 2004, 75:2, 229–235

Bibliographic databases:

UDC: 517.43+517.5
Received: 18.12.2001

Citation: G. V. Radzievskii, “Existence Theorems for Momentum Representations Generalized in the Sense of Dzyadyk”, Mat. Zametki, 75:2 (2004), 253–260; Math. Notes, 75:2 (2004), 229–235

Citation in format AMSBIB
\Bibitem{Rad04} \by G.~V.~Radzievskii \paper Existence Theorems for Momentum Representations Generalized in the Sense of Dzyadyk \jour Mat. Zametki \yr 2004 \vol 75 \issue 2 \pages 253--260 \mathnet{http://mi.mathnet.ru/mz31} \crossref{https://doi.org/10.4213/mzm31} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2054556} \zmath{https://zbmath.org/?q=an:1127.47016} \transl \jour Math. Notes \yr 2004 \vol 75 \issue 2 \pages 229--235 \crossref{https://doi.org/10.1023/B:MATN.0000015038.46713.47} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000220006100023} 

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This publication is cited in the following articles:
1. Veselovs'ka H.M., Holub A.P., “Existence Theorems For Multidimensional Generalized Moment Representations”, Ukr. Math. J., 69:4 (2017), 534–545
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