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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 303, Pages 145–160
(Mi znsl905)
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This article is cited in 14 scientific papers (total in 14 papers)
Some applications of Duhamel product
M. T. Karaev Suleyman Demirel University
Abstract:
The Duhamel product of functions $f$ and $g$ is defined by formula
$$
(f\circledast g)(x)=\frac{d}{dx}\int^x_0 f(x-t)g(t)\,dt.
$$
In the present paper the Duhamel product is used in the study of the spectral multiplicity for direct sums of operators and in the description of cyclic vectors of the restriction of the integration operator in two variables $f(x,y)\mapsto\int^x_0\int^y_0 f(t,\tau)d\tau\,dt$ to its invariant subspace consisting of functions that depend only on the product $xy$.
Received: 25.06.2003
Citation:
M. T. Karaev, “Some applications of Duhamel product”, Investigations on linear operators and function theory. Part 31, Zap. Nauchn. Sem. POMI, 303, POMI, St. Petersburg, 2003, 145–160; J. Math. Sci. (N. Y.), 129:4 (2005), 4009–4017
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https://www.mathnet.ru/eng/znsl905 https://www.mathnet.ru/eng/znsl/v303/p145
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Abstract page: | 393 | Full-text PDF : | 108 | References: | 55 |
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