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Mat. Sb. (N.S.), 1974, Volume 95(137), Number 4(12), Pages 560–587 (Mi msb3769)  

This article is cited in 15 scientific papers (total in 16 papers)

Differential and pseudodifferential operators in spaces of almost periodic functions

M. A. Shubin


Abstract: We construct a Sobolev-type space of almost periodic functions, in which we study differential and pseudodifferential operators. We show that the usual theorem on the regularity of solutions of elliptic equations is not true in these spaces, and we present modified variants of this theorem. We also study the question of the defect indices of differential operators in the space of Besicovitch almost periodic functions, and prove a Liouville-type theorem in this space.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 24:4, 547–573

Bibliographic databases:

UDC: 517.43
MSC: Primary 35J30, 35D05, 35S05, 47F05, 47G05, 42A84; Secondary 46E35
Received: 29.05.1974

Citation: M. A. Shubin, “Differential and pseudodifferential operators in spaces of almost periodic functions”, Mat. Sb. (N.S.), 95(137):4(12) (1974), 560–587; Math. USSR-Sb., 24:4 (1974), 547–573

Citation in format AMSBIB
\Bibitem{Shu74}
\by M.~A.~Shubin
\paper Differential and pseudodifferential operators in spaces of almost periodic functions
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 95(137)
\issue 4(12)
\pages 560--587
\mathnet{http://mi.mathnet.ru/msb3769}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=358445}
\zmath{https://zbmath.org/?q=an:0311.47022}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 24
\issue 4
\pages 547--573
\crossref{https://doi.org/10.1070/SM1974v024n04ABEH001923}


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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. M. A. Shubin, “Almost-periodic elliptic operators and von Neumann algebras”, Funct. Anal. Appl., 9:1 (1975), 88–89  mathnet  crossref  mathscinet  zmath
    2. V. I. Bezyaev, “Asymptotics of the density of states of hypoelliptic almost periodic operators”, Math. USSR-Sb., 34:4 (1978), 425–447  mathnet  crossref  mathscinet  zmath
    3. B. V. Fedosov, M. A. Shubin, “The index of random elliptic operators. II”, Math. USSR-Sb., 35:1 (1979), 131–156  mathnet  crossref  mathscinet  zmath  isi
    4. M. A. Shubin, “Almost periodic functions and partial differential operators”, Russian Math. Surveys, 33:2 (1978), 1–52  mathnet  crossref  mathscinet  zmath
    5. M. A. Shubin, “The spectral theory and the index of elliptic operators with almost periodic coefficients”, Russian Math. Surveys, 34:2 (1979), 109–157  mathnet  crossref  mathscinet  zmath
    6. A. S. Mishchenko, “Banach algebras, pseudodifferential operators, and their application to $K$-theory”, Russian Math. Surveys, 34:6 (1979), 77–91  mathnet  crossref  mathscinet  zmath
    7. P. E. Dedik, M. A. Shubin, “Random pseudodifferential operators and the stabilization of solutions of parabolic equations with random coefficients”, Math. USSR-Sb., 41:1 (1982), 33–52  mathnet  crossref  mathscinet  zmath
    8. Bruno Scarpellini, Pierre-A. Vuillermot, “Smooth manifolds for semilinear wave equations on 2: On the existence of almost-periodic breathers”, Journal of Differential Equations, 77:1 (1989), 123  crossref  mathscinet  zmath
    9. Pierre-A Vuillermot, “Almost-periodic attractors for a class of nonautonomous reaction-diffusion equations on N. I. Global stabilization processes”, Journal of Differential Equations, 94:2 (1991), 228  crossref  mathscinet  zmath
    10. Pierre-A. Vuillermot, “Almost-periodic attractors for a class of nonautonomous reaction-diffusion equations on N—III. Center curves and liapounov stability”, Nonlinear Analysis: Theory, Methods & Applications, 22:5 (1994), 533  crossref  mathscinet  zmath
    11. Alessandro Oliaro, Luigi Rodino, Patrik Wahlberg, “Almost periodic pseudodifferential operators and Gevrey classes”, Annali di Matematica, 2011  crossref  mathscinet
    12. Patrik Wahlberg, “Representations of almost periodic pseudodifferential operators and applications in spectral theory”, J. Pseudo-Differ. Oper. Appl, 2011  crossref  mathscinet
    13. Desheng Ji, Chuanyi Zhang, “Pseudo almost periodic weak solutions of a semilinear elliptic equation”, Adv Diff Equ, 2014:1 (2014), 46  crossref  mathscinet  zmath
    14. N. Bodendorfer, “Quantum reduction to Bianchi I models in loop quantum gravity”, Phys. Rev. D, 91:8 (2015)  crossref  mathscinet
    15. Paolo Boggiatto, Carmen Fernández, Antonio Galbis, “Gabor systems and almost periodic functions”, Applied and Computational Harmonic Analysis, 2015  crossref  mathscinet
    16. M. Braverman, V. M. Bukhshtaber, M. Gromov, V. Ivrii, Yu. A. Kordyukov, P. Kuchment, V. Mazya, S. P. Novikov, T. Sunada, L. Fridlender, A. G. Khovanskii, “Mikhail Aleksandrovich Shubin (nekrolog)”, UMN, 75:6(456) (2020), 162–170  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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