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Mat. Zametki, 2003, Volume 73, Issue 2, Pages 179–194 (Mi mz188)  

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

Joint Approximations of Distributions in Banach Spaces

A. M. Voroncov

M. V. Lomonosov Moscow State University

Abstract: For a given homogeneous elliptic partial differential operator $L$ with constant complex coefficients, two Banach spaces $V_1$ and $V_2$ of distributions in $\mathbb R^N$, and compact sets $X_1$ and $X_2$ in $\mathbb R^N$, we study joint approximations in the norms of the spaces $V_1(X_1)$ and $V_2(X_2)$ (the spaces of Whitney jet-distributions) by the solutions of the equation $L_u=0$ in neighborhoods of the set $X_1\cup X_2$. We obtain a localization theorem, which, under certain conditions, allows one to reduce the above-cited approximation problem to the corresponding separate problems in each of the spaces.

DOI: https://doi.org/10.4213/mzm188

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English version:
Mathematical Notes, 2003, 73:2, 168–182

Bibliographic databases:

UDC: 517.988
Received: 09.04.2002

Citation: A. M. Voroncov, “Joint Approximations of Distributions in Banach Spaces”, Mat. Zametki, 73:2 (2003), 179–194; Math. Notes, 73:2 (2003), 168–182

Citation in format AMSBIB
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\by A.~M.~Voroncov
\paper Joint Approximations of Distributions in Banach Spaces
\jour Mat. Zametki
\yr 2003
\vol 73
\issue 2
\pages 179--194
\mathnet{http://mi.mathnet.ru/mz188}
\crossref{https://doi.org/10.4213/mzm188}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1997658}
\zmath{https://zbmath.org/?q=an:1037.46038}
\transl
\jour Math. Notes
\yr 2003
\vol 73
\issue 2
\pages 168--182
\crossref{https://doi.org/10.1023/A:1022150807169}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000181384200020}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Voroncov, “Estimates of $C^m$-Capacity of Compact Sets in $\mathbb{R}^N$”, Math. Notes, 75:6 (2004), 751–764  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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