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Mat. Zametki, 1977, Volume 21, Issue 5, Pages 677–689 (Mi mz7999)  

This article is cited in 7 scientific papers (total in 7 papers)

Fundamental functions vanishing on a given set and division by functions

S. G. Samko

Rostov State University

Abstract: The space $\Psi_V$ of fundamental functions (a subspace of S) consisting of functions vanishing together with all their derivatives on a given closed set $V\subset R^n$ is constructed. Multipliers in $\Psi_V$ are described. In the space $\Psi_V$ is easily realized the division of unity by an infinitely differentiable function, “vanishing slowly” for approximation to its zero set, (in particular, by a polynomial). In the case of a cone $V$ in $R^n$, a description of the dual space $\Phi_V$ consisting of the Fourier preimages of functions of $\Psi_V$ is given. The problem of multipliers in $\Phi_V$ is discussed.

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English version:
Mathematical Notes, 1977, 21:5, 379–386

Bibliographic databases:

UDC: 517.9
Received: 17.04.1975

Citation: S. G. Samko, “Fundamental functions vanishing on a given set and division by functions”, Mat. Zametki, 21:5 (1977), 677–689; Math. Notes, 21:5 (1977), 379–386

Citation in format AMSBIB
\Bibitem{Sam77}
\by S.~G.~Samko
\paper Fundamental functions vanishing on a~given set and division by functions
\jour Mat. Zametki
\yr 1977
\vol 21
\issue 5
\pages 677--689
\mathnet{http://mi.mathnet.ru/mz7999}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=482170}
\zmath{https://zbmath.org/?q=an:0398.46033|0362.46030}
\transl
\jour Math. Notes
\yr 1977
\vol 21
\issue 5
\pages 379--386
\crossref{https://doi.org/10.1007/BF01788235}


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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. V. A. Nogin, “The weighted spaces $L^\alpha_{p,r}(\rho_1,\rho_2)$ of differentiable functions of fractional smoothness”, Math. USSR-Sb., 59:1 (1988), 209–221  mathnet  crossref  mathscinet  zmath
    2. A. N. Karapetyants, V. A. Nogin, “Characterization of functions in anisotropic spaces of complex order”, Russian Math. (Iz. VUZ), 42:5 (1998), 22–28  mathnet  mathscinet  elib
    3. V. A. Nogin, K. S. Shevchenko, “Inversion of some Riesz potentials with oscillating characteristics in the nonelliptic case”, Russian Math. (Iz. VUZ), 43:10 (1999), 74–77  mathnet  mathscinet  zmath
    4. M. A. Betilgiriev, D. N. Karasev, V. A. Nogin, “Opisanie obraza odnogo operatora tipa potentsiala s ostsilliruyuschim yadrom”, Vladikavk. matem. zhurn., 7:2 (2005), 17–25  mathnet  mathscinet
    5. Marc Troyanov, “On the Hodge decomposition in $\mathbb R^n$”, Mosc. Math. J., 9:4 (2009), 899–926  mathnet  crossref  mathscinet  zmath
    6. A. V. Gil, V. A. Nogin, “Obraschenie i opisanie obrazov potentsialov s osobennostyami yader na sfere”, Vladikavk. matem. zhurn., 14:4 (2012), 10–18  mathnet
    7. E. L. Shishkina, “Obschee uravnenie Eilera—Puassona—Darbu i giperbolicheskie $B$-potentsialy”, Uravneniya v chastnykh proizvodnykh, SMFN, 65, no. 2, Rossiiskii universitet druzhby narodov, M., 2019, 157–338  mathnet  crossref
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