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Sbornik: Mathematics, 1997, Volume 188, Issue 2, Pages 195–226
DOI: https://doi.org/10.1070/SM1997v188n02ABEH000200
(Mi sm200)
 

This article is cited in 3 scientific papers (total in 4 papers)

The fundamental principle for invariant subspaces of analytic functions. I

I. F. Krasichkov-Ternovskii

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
References:
Abstract: Let W be a differentiation-invariant subspace of the topological product H=H(G1)××H(Gq) of the spaces of analytic functions in domains G1,,Gq in C, respectively. Under certain assumptions there exists a sequence of complex numbers {λi}, i=1,2,, and projection operators pi:WW(λi) onto the root subspaces W(λi)W corresponding to the eigenvalues λi of the differentiation operator. This enables one to associate with each element fW the formal series fpi(f). The fundamental principle is the phenomenon of the convergence of this series to the corresponding element f for each f in W. The existence of the projections pi depends on a particular property of the annihilator submodule of W: its stability with respect to division by binomials zλ. Stability questions arising in establishing the fundamental principle are considered.
Received: 23.01.1996
Bibliographic databases:
UDC: 517.5
MSC: 46E10, 30B99
Language: English
Original paper language: Russian
Citation: I. F. Krasichkov-Ternovskii, “The fundamental principle for invariant subspaces of analytic functions. I”, Sb. Math., 188:2 (1997), 195–226
Citation in format AMSBIB
\Bibitem{Kra97}
\by I.~F.~Krasichkov-Ternovskii
\paper The fundamental principle for invariant subspaces of analytic functions.~I
\jour Sb. Math.
\yr 1997
\vol 188
\issue 2
\pages 195--226
\mathnet{http://mi.mathnet.ru/eng/sm200}
\crossref{https://doi.org/10.1070/SM1997v188n02ABEH000200}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1453258}
\zmath{https://zbmath.org/?q=an:0903.46022}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1997XE98900010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0031287034}
Linking options:
  • https://www.mathnet.ru/eng/sm200
  • https://doi.org/10.1070/SM1997v188n02ABEH000200
  • https://www.mathnet.ru/eng/sm/v188/i2/p25
    Cycle of papers
    This publication is cited in the following 4 articles:
    1. S. G. Merzlyakov, “Systems of convolution equations in complex domains”, Ufa Math. J., 10:2 (2018), 78–92  mathnet  crossref  isi
    2. “Igor Fedorovich Krasichkov-Ternovskii (13.02.1935–08.03.2012)”, Ufimsk. matem. zhurn., 4:3 (2012), 187–192  mathnet
    3. I. F. Krasichkov-Ternovskii, “The fundamental principle for invariant subspaces of analytic functions. II”, Sb. Math., 188:6 (1997), 853–892  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. I. F. Krasichkov-Ternovskii, “The fundamental principle for invariant subspaces of analytic functions. III”, Sb. Math., 188:10 (1997), 1439–1479  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:612
    Russian version PDF:222
    English version PDF:26
    References:108
    First page:1
     
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