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Zapiski Nauchnykh Seminarov POMI, 1998, Volume 255, Pages 5–16
(Mi znsl929)
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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
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
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
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https://www.mathnet.ru/eng/znsl929 https://www.mathnet.ru/eng/znsl/v255/p5
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Abstract page: | 175 | Full-text PDF : | 63 |
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