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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 4, Pages 768–793 (Mi izv1865)  

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

Of Volterra operators in the scale $L_p[0,1]$ $(1\leqslant p\leqslant\infty)$

M. M. Malamud, È. R. Tsekanovskii


Abstract: In this article a method of a priori estimates is used to solve an integro-differential equation and to substantially strengthen previously obtained sufficient conditions for the operator $\mathscr Kf=i\int_0^xk(x,t)f(t) dt$ to be similar to the operator $\mathscr Tf=i\int_0^xf(t) dt$ in the scale $L_p[0,1]$. Criteria for the similarity of $\mathscr K$ to $\mathscr T$ are found for a wide class of kernels which depend on a difference.
Bibliography: 17 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:4, 725–748

Bibliographic databases:

UDC: 513.88
MSC: Primary 47G05; Secondary 45K05
Received: 30.12.1974

Citation: M. M. Malamud, È. R. Tsekanovskii, “Of Volterra operators in the scale $L_p[0,1]$ $(1\leqslant p\leqslant\infty)$”, Izv. Akad. Nauk SSSR Ser. Mat., 41:4 (1977), 768–793; Math. USSR-Izv., 11:4 (1977), 725–748

Citation in format AMSBIB
\Bibitem{MalTse77}
\by M.~M.~Malamud, \`E.~R.~Tsekanovskii
\paper Of Volterra operators in the scale $L_p[0,1]$ $(1\leqslant p\leqslant\infty)$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 4
\pages 768--793
\mathnet{http://mi.mathnet.ru/izv1865}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=473924}
\zmath{https://zbmath.org/?q=an:0367.45003}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 4
\pages 725--748
\crossref{https://doi.org/10.1070/IM1977v011n04ABEH001743}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Lev Khazanovich, “The elastic–viscoelastic correspondence principle for non-homogeneous materials with time translation non-invariant properties”, International Journal of Solids and Structures, 45:17 (2008), 4739  crossref  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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