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

This article is cited in 3 scientific papers (total in 3 papers)

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
Received: 16.08.2012

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
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\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
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. S. N. Mishin, “Homogeneous differential-operator equations in locally convex spaces”, Russian Math. (Iz. VUZ), 61:1 (2017), 22–38  mathnet  crossref  isi
    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  mathnet  crossref  crossref  isi  elib
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