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

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

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
\Bibitem{Vor03} \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} 

• http://mi.mathnet.ru/eng/mz188
• https://doi.org/10.4213/mzm188
• http://mi.mathnet.ru/eng/mz/v73/i2/p179

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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
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