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



Probl. Peredachi Inf.:
Year:
Volume:
Issue:
Page:
Find






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


Probl. Peredachi Inf., 2015, Volume 51, Issue 3, Pages 41–69 (Mi ppi2179)  

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

Methods of Signal Processing

Strong divergence for system approximations

H. Bochea, U. J. Mönichb

a Technische Universität München, Lehrstuhl für Theoretische Informationstechnik, Germany, Germany
b Massachusetts Institute of Technology, Research Laboratory of Electronics, New York, USA

Abstract: In this paper we analyze approximation of stable linear time-invariant systems, like the Hilbert transform, by sampling series for bandlimited functions in the Paley–Wiener space $\mathcal{PW}_\pi^1$. It is known that there exist systems and functions such that the approximation process is weakly divergent, i.e., divergent for certain subsequences. Here we strengthen this result by proving strong divergence, i.e., divergence for all subsequences. Further, in case of divergence, we give the divergence speed. We consider sampling at Nyquist rate as well as oversampling with adaptive choice of the kernel. Finally, connections between strong divergence and the Banach–Steinhaus theorem, which is not powerful enough to prove strong divergence, are discussed.

Full text: PDF file (325 kB)
References: PDF file   HTML file

English version:
Problems of Information Transmission, 2015, 51:3, 240–266

Bibliographic databases:

UDC: 621.391.1+517
Received: 03.01.2015

Citation: H. Boche, U. J. Mönich, “Strong divergence for system approximations”, Probl. Peredachi Inf., 51:3 (2015), 41–69; Problems Inform. Transmission, 51:3 (2015), 240–266

Citation in format AMSBIB
\Bibitem{BocMon15}
\by H.~Boche, U.~J.~M\"onich
\paper Strong divergence for system approximations
\jour Probl. Peredachi Inf.
\yr 2015
\vol 51
\issue 3
\pages 41--69
\mathnet{http://mi.mathnet.ru/ppi2179}
\transl
\jour Problems Inform. Transmission
\yr 2015
\vol 51
\issue 3
\pages 240--266
\crossref{https://doi.org/10.1134/S0032946015030047}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000363254900004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84944447229}


Linking options:
  • http://mi.mathnet.ru/eng/ppi2179
  • http://mi.mathnet.ru/eng/ppi/v51/i3/p41

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. H. Boche, V. Pohl, “On the Strong Divergence of Hilbert Transform Approximations and a Problem of Ul'yanov”, J. Approx. Theory, 204 (2016), 34–60  crossref  zmath  isi  elib  scopus
  • Проблемы передачи информации Problems of Information Transmission
    Number of views:
    This page:166
    Full text:15
    References:54
    First page:48

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020