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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 4, Pages 868–894 (Mi izv1871)  

This article is cited in 5 scientific papers (total in 6 papers)

Theorems of Paley–Wiener and Müntz–Szász type

M. M. Dzhrbashyan, V. M. Martirosyan


Abstract: In the paper a new integral representation of the well-known function classes $\mathscr H_2[\alpha]$ ($0<\alpha<1$) is established, which in the limiting case $\alpha=1$ goes into the Paley–Wiener theorem. A Hilbert space metric is introduced into the classes $\mathscr H_2[\alpha]$ ($0<\alpha<+\infty$), and a criterion for closedness of certain systems of functions in these spaces is established. In particular, a theorem of Müntz–Szász type in the complex domain is proved, and a complete intrinsic description is given of the corresponding nonclosed systems.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:4, 821–847

Bibliographic databases:

UDC: 517.5
MSC: 30A78, 30A86, 30A18
Received: 14.01.1976

Citation: M. M. Dzhrbashyan, V. M. Martirosyan, “Theorems of Paley–Wiener and Müntz–Szász type”, Izv. Akad. Nauk SSSR Ser. Mat., 41:4 (1977), 868–894; Math. USSR-Izv., 11:4 (1977), 821–847

Citation in format AMSBIB
\Bibitem{DzhMar77}
\by M.~M.~Dzhrbashyan, V.~M.~Martirosyan
\paper Theorems of Paley--Wiener and M\"untz--Sz\'asz type
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 4
\pages 868--894
\mathnet{http://mi.mathnet.ru/izv1871}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=473707}
\zmath{https://zbmath.org/?q=an:0362.30004}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 4
\pages 821--847
\crossref{https://doi.org/10.1070/IM1977v011n04ABEH001747}


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    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. N. U. Arakelian, A. G. Vitushkin, V. S. Vladimirov, A. A. Gonchar, “Mkhitar Mkrtichevich Dzhrbashyan (on his sixtieth birthday)”, Russian Math. Surveys, 34:2 (1979), 269–275  mathnet  crossref  mathscinet  zmath
    2. M. M. Dzhrbashyan, “A characterization of the closed linear spans of two families of incomplete systems of analitic functions”, Math. USSR-Sb., 42:1 (1982), 1–70  mathnet  crossref  mathscinet  zmath
    3. R.A. Zalik, “Remarks on a paper of Gel'fand and S̆ilov on Fourier transforms”, Journal of Mathematical Analysis and Applications, 102:1 (1984), 102  crossref
    4. Michael Niggemann, “An isomorphism of Paley-Wiener type”, Journal of Mathematical Analysis and Applications, 118:2 (1986), 395  crossref
    5. I. M. Guseinov, “On a Representation of the Jost Solution for Ordinary Differential Equations”, Funct. Anal. Appl., 33:3 (1999), 222–224  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. A A Nabiev, “Inverse scattering problem for the Schrödinger-type equation with a polynomial energy-dependent potential”, Inverse Probl, 22:6 (2006), 2055  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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