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 Ufimsk. Mat. Zh., 2013, Volume 5, Issue 1, Pages 112–124 (Mi ufa191)

On growth characteristics of operator-valued functions

S. N. Mishin

Orel State University

Abstract: In the work Liouville theorem and the concept of order and type of entire function are generalized to the case of operator-valued function with values in the space $\mathrm{Lec}(\mathbf{H}_1,\mathbf{H})$ of all linear continuous operators acting from a locally convex space $\mathbf{H}_1$ to a locally convex space $\mathbf{H}$ with equicontinuous bornology. We find the formulae expressing the order and type of operator-valued function in terms of characteristics of the sequence of coefficients. Some properties of order and type of operator-valued function are established.

Keywords: locally convex space, order and type of sequence of operators, order and type of entire function, equicontinuous bornology, convergence by bornology, operator-valued function.

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English version:
Ufa Mathematical Journal, 2013, 5:1, 112–124 (PDF, 403 kB); https://doi.org/10.13108/2013-5-1-112

Bibliographic databases:

UDC: 517.98+517.53

Citation: S. N. Mishin, “On growth characteristics of operator-valued functions”, Ufimsk. Mat. Zh., 5:1 (2013), 112–124; Ufa Math. J., 5:1 (2013), 112–124

Citation in format AMSBIB
\Bibitem{Mis13} \by S.~N.~Mishin \paper On growth characteristics of operator-valued functions \jour Ufimsk. Mat. Zh. \yr 2013 \vol 5 \issue 1 \pages 112--124 \mathnet{http://mi.mathnet.ru/ufa191} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3429955} \elib{http://elibrary.ru/item.asp?id=18929631} \transl \jour Ufa Math. J. \yr 2013 \vol 5 \issue 1 \pages 112--124 \crossref{https://doi.org/10.13108/2013-5-1-112} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. S. N. Mishin, “Invariance of the Order and Type of a Sequence of Operators”, Math. Notes, 100:3 (2016), 429–437
2. S. N. Mishin, “Homogeneous differential-operator equations in locally convex spaces”, Russian Math. (Iz. VUZ), 61:1 (2017), 22–38
3. S. N. Mishin, “Generalization of the Lagrange Method to the Case of Second-Order Linear Differential Equations with Constant Operator Coefficients in Locally Convex Spaces”, Math. Notes, 103:1 (2018), 75–88
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