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Zapiski Nauchnykh Seminarov POMI, 1998, Volume 255, Pages 5–16 (Mi znsl929)  

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

Integrals of scalar functions against a vector measure and their applications to some questions of functional analysis and linear integral equations

G. Ya. Areshkin

Military Technical University
Full-text PDF (206 kB) Citations (1)
Abstract: We prove some assertions on the decomposition of indefinite integrals of scalar functions against a vector measure, as well as of continuous linear operators acting from a fundamental Banach space $X(T,\Sigma,\mu)$ to a Hilbert space $H$. Hence we deduce a representation theorem for continuous linear operators going from $X$ to $H$. These results are applied to most general linear integral equations of the form $\int\limits_Tx(t)d\nu=\varphi$, $x\in X$, $\varphi\in H$, $\nu\colon\Sigma\to H$, $\nu\ll\mu$. Such equations are equivalent to certain infinite systems of scalar integral equations and to infinite systems of linear algebraic equations.
Received: 12.01.1998
English version:
Journal of Mathematical Sciences (New York), 2001, Volume 107, Issue 4, Pages 3963–3971
DOI: https://doi.org/10.1023/A:1012458013901
Bibliographic databases:
UDC: 517.98
Language: Russian
Citation: G. Ya. Areshkin, “Integrals of scalar functions against a vector measure and their applications to some questions of functional analysis and linear integral equations”, Investigations on linear operators and function theory. Part 26, Zap. Nauchn. Sem. POMI, 255, POMI, St. Petersburg, 1998, 5–16; J. Math. Sci. (New York), 107:4 (2001), 3963–3971
Citation in format AMSBIB
\Bibitem{Are98}
\by G.~Ya.~Areshkin
\paper Integrals of scalar functions against a vector measure and their applications to some questions of functional
analysis and linear integral equations
\inbook Investigations on linear operators and function theory. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 1998
\vol 255
\pages 5--16
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl929}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1692869}
\zmath{https://zbmath.org/?q=an:0980.46032}
\transl
\jour J. Math. Sci. (New York)
\yr 2001
\vol 107
\issue 4
\pages 3963--3971
\crossref{https://doi.org/10.1023/A:1012458013901}
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  • https://www.mathnet.ru/eng/znsl/v255/p5
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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