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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 6, Pages 1289–1328 (Mi izv2071)  

This article is cited in 11 scientific papers (total in 12 papers)

Lack of interpolation of linear operators in spaces of smooth functions

B. S. Mityagin, E. M. Semenov


Abstract: We prove that $C^k(\Omega)$, the space of $k$ times continuously differentiable functions on the closure of a region in a finite-dimensional manifold, is not an interpolation space between $C(\Omega)$ and $C^n(\Omega)$ for $0<k<n$. We find analogous results for the Sobolev–Stein spaces. In the class of spaces $C_\varphi$, defined by the modulus of continuity, we describe all interpolation spaces between $C$ and $C^2$.
Bibliography: 34 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:6, 1229–1266

Bibliographic databases:

UDC: 513.88
MSC: Primary 43A15, 46E15, 46E35; Secondary 26A15, 32E10, 47G05
Received: 13.07.1976

Citation: B. S. Mityagin, E. M. Semenov, “Lack of interpolation of linear operators in spaces of smooth functions”, Izv. Akad. Nauk SSSR Ser. Mat., 41:6 (1977), 1289–1328; Math. USSR-Izv., 11:6 (1977), 1229–1266

Citation in format AMSBIB
\Bibitem{MitSem77}
\by B.~S.~Mityagin, E.~M.~Semenov
\paper Lack of interpolation of linear operators in spaces of smooth functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 6
\pages 1289--1328
\mathnet{http://mi.mathnet.ru/izv2071}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=482148}
\zmath{https://zbmath.org/?q=an:0369.46033|0395.46030}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 6
\pages 1229--1266
\crossref{https://doi.org/10.1070/IM1977v011n06ABEH001767}


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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. Heinz H. Gonska, “On approximation in spaces of continuous functions”, BAZ, 28:3 (1983), 411  crossref
    2. Claudia Cottin, “MixedK-functionals: A measure of smoothness for blending-type approximation”, Math Z, 204:1 (1990), 69  crossref  mathscinet  zmath  isi
    3. Lech Maligranda, Lars Erik Persson, “The E-Functional for Some Pairs of Groups”, Results. Math, 20:1-2 (1991), 538  crossref
    4. C. Badea, “K-functionals and moduli of smoothness of functions defined on compact metric spaces”, Computers & Mathematics with Applications, 30:3-6 (1995), 23  crossref
    5. S. V. Astashkin, S. M. Nikol'skii, S. Ya. Novikov, “Evgenii Mikhailovich Semenov (on his 60th birthday)”, Russian Math. Surveys, 56:6 (2001), 1193–1198  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. Carlo Bardaro, Ilaria Mantellini, “A Quantitative Voronovskaya Formula for Mellin Convolution Operators”, Mediterr j math, 2010  crossref
    7. Carlo Bardaro, Ilaria Mantellini, “Generalized Sampling Approximation of Bivariate Signals: Rate of Pointwise Convergence”, Num. Functional Analysis & Optimization, 31:2 (2010), 131  crossref
    8. Carlo Bardaro, Ilaria Mantellini, “A quantitative asymptotic formula for a general class of discrete operators”, Computers & Mathematics with Applications, 60:10 (2010), 2859  crossref
    9. A. M. Acu, H. Gonska, I. Raşa, “Grüss-type and Ostrowski-type inequalities in approximation theory”, Ukr Math J, 2011  crossref
    10. Gancho T. Tachev, “The complete asymptotic expansion for Bernstein operators”, Journal of Mathematical Analysis and Applications, 385:2 (2012), 1179  crossref
    11. Bogdan Gavrea, “Improvement of some inequalities of Chebysev–Grüss type”, Computers & Mathematics with Applications, 2012  crossref
    12. Heiner Gonska, Ioan Raşa, Maria-Daniela Rusu, “Čebyšev-Grüss-type inequalities revisited”, Math. Slovaca, 63:5 (2013), 1007  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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