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Sbornik: Mathematics, 1998, Volume 189, Issue 9, Pages 1423–1440
DOI: https://doi.org/10.1070/sm1998v189n09ABEH000355
(Mi sm355)
 

This article is cited in 13 scientific papers (total in 13 papers)

Spectral synthesis for systems of differential operators with constant coefficients. Duality theorem

A. B. Shishkin

Armavir State Pedagogical Institute
References:
Abstract: Most known papers on spectral synthesis in complex domains are based on transitions from problems of spectral synthesis to equivalent problems of local description. As a rule, such a transition is carried out in the framework of some special assumptions and meets considerable difficulties. A general method developed in this paper enables one to verify the duality theorem in the setting of several complex variables, when each operator πp(D), p=1,,q, acts with respect to a single variable. These assumptions cover the case of a system of partial differential operators. The duality transition here breaks into three separate steps. Two of them are connected with classical results of the theory of analytic functions and only one relates to general duality theory. This allows one to speak about singling out the analytic component of the transition from a spectral synthesis problem to an equivalent problem of local description.
Received: 05.07.1996 and 08.05.1998
Bibliographic databases:
UDC: 517.5
MSC: Primary 47E05; Secondary 34L05, 46E10
Language: English
Original paper language: Russian
Citation: A. B. Shishkin, “Spectral synthesis for systems of differential operators with constant coefficients. Duality theorem”, Sb. Math., 189:9 (1998), 1423–1440
Citation in format AMSBIB
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\by A.~B.~Shishkin
\paper Spectral synthesis for systems of differential operators with constant coefficients. Duality theorem
\jour Sb. Math.
\yr 1998
\vol 189
\issue 9
\pages 1423--1440
\mathnet{http://mi.mathnet.ru/eng/sm355}
\crossref{https://doi.org/10.1070/sm1998v189n09ABEH000355}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1687011}
\zmath{https://zbmath.org/?q=an:0923.47025}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0039504345}
Linking options:
  • https://www.mathnet.ru/eng/sm355
  • https://doi.org/10.1070/sm1998v189n09ABEH000355
  • https://www.mathnet.ru/eng/sm/v189/i9/p143
  • This publication is cited in the following 13 articles:
    1. A. B. Shishkin, “On continuous endomorphisms of entire functions”, Sb. Math., 212:4 (2021), 567–591  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
    2. A. B. Shishkin, “Odnostoronnie skhemy dvoistvennosti”, Vladikavk. matem. zhurn., 22:3 (2020), 124–150  mathnet  crossref
    3. A. B. Shishkin, “Symmetric representations of holomorphic functions”, Probl. anal. Issues Anal., 7(25), spetsvypusk (2018), 124–136  mathnet  crossref  elib
    4. Krantz S., “Harmonic and Complex Analysis in Several Variables”, Harmonic and Complex Analysis in Several Variables, Springer Monographs in Mathematics, Springer, 2017, 1–424  crossref  mathscinet  isi
    5. A. B. Shishkin, “Proektivnoe i in'ektivnoe opisaniya v kompleksnoi oblasti. Dvoistvennost”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 14:1 (2014), 47–65  mathnet  crossref  elib
    6. T. A. Volkovaya, “Sintez v polinomialnom yadre dvukh analiticheskikh funktsionalov”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 14:3 (2014), 251–262  mathnet  crossref  elib
    7. T. A. Volkovaya, A. B. Shishkin, “Lokalnoe opisanie tselykh funktsii. Podmoduli ranga 1”, Vladikavk. matem. zhurn., 16:2 (2014), 14–28  mathnet
    8. A. P. Khromov, “Finite-dimensional perturbations of Volterra operators”, Journal of Mathematical Sciences, 138:5 (2006), 5893–6066  mathnet  crossref  mathscinet  zmath  elib
    9. I. F. Krasichkov-Ternovskii, “Approximation theorem for a homogeneous vector convolution equation”, Sb. Math., 195:9 (2004), 1271–1289  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. I. F. Krasichkov-Ternovskii, “Spectral synthesis and analytic continuation”, Russian Math. Surveys, 58:1 (2003), 31–108  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. A. B. Shishkin, “Spectral synthesis for systems of differential operators with constant coefficients”, Sb. Math., 194:12 (2003), 1865–1898  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. I. F. Krasichkov-Ternovskii, A. B. Shishkin, “Local description of closed submodules of a special module of entire functions of exponential type”, Sb. Math., 192:11 (2001), 1621–1638  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. I. F. Krasichkov-Ternovskii, “Spectral synthesis and local description for several variables”, Izv. Math., 63:4 (1999), 729–755  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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