Zapiski Nauchnykh Seminarov POMI
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zapiski Nauchnykh Seminarov POMI, 1994, Volume 217, Pages 92–111 (Mi znsl5963)  

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

Spectral synthesis in the Sobolev space associated with integral metric

Yu. V. Netrusov

St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences
Full-text PDF (753 kB) Citations (1)
Abstract: The aim of this paper is to prove Theorem A.
Theorem A. Let $l\in\mathbb N$, $A\subset\mathbb R^n$. Then the following two conditions are equivalent:
1) for any $\varepsilon>0$ there exist a function $f_\varepsilon$ and an open set $G\supset A$ such that

$$ \operatorname{supp}f_\varepsilon\subset\mathbb R^n\setminus G,\qquad\|f-f_\varepsilon\|_{W^l_1}\le\varepsilon; $$

2) for any $\alpha=(\alpha_1,\dots,\alpha_n)\in\{0,1,2,\dots,\}^n$, $|\alpha|=\alpha_1+\dots+\alpha_n<l$, there exists a set $E_\alpha$ with the following properties:
a) if $n\le l-|\alpha|$ then $E_\alpha=A$;
b) if $n>l-|\alpha|$ then the Hausdorff measure of order $n-l+|\alpha|$ of set $A\setminus E_\alpha$ is equal to zero;
c) for any point $x\in E_\alpha$ the following relation holds:

$$ \lim_{a\to0}a^{-n}\int_{D(x,a)}|D^\alpha f(y)|\,dy=0, $$
where $D(x,a)$ is the ball of radius $a>0$ centered at $x\in\mathbb R^n$.
Some generalizations of this result are also proved. Bibliography: 9 titles.
Received: 15.02.1994
English version:
Journal of Mathematical Sciences (New York), 1997, Volume 85, Issue 2, Pages 1814–1826
DOI: https://doi.org/10.1007/BF02355292
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: Yu. V. Netrusov, “Spectral synthesis in the Sobolev space associated with integral metric”, Investigations on linear operators and function theory. Part 22, Zap. Nauchn. Sem. POMI, 217, POMI, St. Petersburg, 1994, 92–111; J. Math. Sci. (New York), 85:2 (1997), 1814–1826
Citation in format AMSBIB
\Bibitem{Net94}
\by Yu.~V.~Netrusov
\paper Spectral synthesis in the Sobolev space associated with integral metric
\inbook Investigations on linear operators and function theory. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 1994
\vol 217
\pages 92--111
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5963}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1327518}
\zmath{https://zbmath.org/?q=an:0882.46016|0907.46029}
\transl
\jour J. Math. Sci. (New York)
\yr 1997
\vol 85
\issue 2
\pages 1814--1826
\crossref{https://doi.org/10.1007/BF02355292}
Linking options:
  • https://www.mathnet.ru/eng/znsl5963
  • https://www.mathnet.ru/eng/znsl/v217/p92
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
    Statistics & downloads:
    Abstract page:154
    Full-text PDF :67
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024