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Uspekhi Mat. Nauk, 1978, Volume 33, Issue 2(200), Pages 3–47 (Mi umn3388)  

This article is cited in 36 scientific papers (total in 36 papers)

Almost periodic functions and partial differential operators

M. A. Shubin


Full text: PDF file (2728 kB)
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English version:
Russian Mathematical Surveys, 1978, 33:2, 1–52

Bibliographic databases:

UDC: 517.5+517.43
MSC: 47F05, 42A75, 42A05, 35B65, 35Sxx, 20Kxx
Received: 11.07.1976

Citation: M. A. Shubin, “Almost periodic functions and partial differential operators”, Uspekhi Mat. Nauk, 33:2(200) (1978), 3–47; Russian Math. Surveys, 33:2 (1978), 1–52

Citation in format AMSBIB
\Bibitem{Shu78}
\by M.~A.~Shubin
\paper Almost periodic functions and partial differential operators
\jour Uspekhi Mat. Nauk
\yr 1978
\vol 33
\issue 2(200)
\pages 3--47
\mathnet{http://mi.mathnet.ru/umn3388}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=636410}
\zmath{https://zbmath.org/?q=an:0383.47025|0408.47039}
\transl
\jour Russian Math. Surveys
\yr 1978
\vol 33
\issue 2
\pages 1--52
\crossref{https://doi.org/10.1070/RM1978v033n02ABEH002303}


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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. 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
    2. 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
    3. V. E. Slyusarchuk, “Bounded solutions of non-linear elliptic equations”, Russian Math. Surveys, 35:1 (1980), 235–236  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. M. A. Antonets, I. A. Shereshevskii, “Weyl quantization on compact Abelian groups and the quantum mechanics of almost periodic systems”, Theoret. and Math. Phys., 48:1 (1981), 597–604  mathnet  crossref  mathscinet  zmath  isi
    5. A. A. Pankov, “Boundedness and almost periodicity in time of solutions of evolutionary variational inequalities”, Math. USSR-Izv., 20:2 (1983), 303–332  mathnet  crossref  mathscinet  zmath
    6. A. A. Pankov, “On bounded and almost-periodic solutions of certain non-linear evolution equations”, Russian Math. Surveys, 37:2 (1982), 239–240  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. A. A. Pankov, “Bounded solutions, almost periodic in time, of a class of nonlinear evolution equations”, Math. USSR-Sb., 49:1 (1984), 73–86  mathnet  crossref  mathscinet  zmath
    8. S. M. Kozlov, M. A. Shubin, “On the coincidence of the spectra of random elliptic operators”, Math. USSR-Sb., 51:2 (1985), 455–471  mathnet  crossref  mathscinet  zmath
    9. M. A. Shubin, “Pseudodifference operators and their Green's functions”, Math. USSR-Izv., 26:3 (1986), 605–622  mathnet  crossref  mathscinet  zmath
    10. B. V. Lange, V. S. Rabinovich, “Pseudodifferential operators on $\mathbf R^n$ and limit operators”, Math. USSR-Sb., 57:1 (1987), 183–194  mathnet  crossref  mathscinet  zmath
    11. Russell A Johnson, “Exponential dichotomy, rotation number, and linear differential operators with bounded coefficients”, Journal of Differential Equations, 61:1 (1986), 54  crossref
    12. O. A. Ladyzhenskaya, “The life and scientific work of Vladimir Ivanovich Smirnov”, Russian Math. Surveys, 42:6 (1987), 1–26  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. M. Sh. Birman, M. Z. Solomyak, “$L_2$-Theory of the Maxwell operator in arbitrary domains”, Russian Math. Surveys, 42:6 (1987), 75–96  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. A. A. Pankov, “Extremal problems with unstabilized integrands”, Funct. Anal. Appl., 22:1 (1988), 70–71  mathnet  crossref  mathscinet  zmath  isi
    15. Ronghui Ji, Jingbo Xia, “On the classification of commutator ideals”, Journal of Functional Analysis, 78:2 (1988), 208  crossref
    16. O. G. Filippov, “On the reduction of pseudodifferential operators with bounded symbols to operators over $C^*$-algebras on compact manifolds”, Russian Math. Surveys, 44:3 (1989), 185–186  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. G. V. Sandrakov, “Averaging principles for eguations with rapidly oscillatory coefficients”, Math. USSR-Sb., 68:2 (1991), 503–553  mathnet  crossref  mathscinet  zmath  isi
    18. 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
    19. A. G. Baskakov, “Wiener's theorem and the asymptotic estimates of the elements of inverse matrices”, Funct. Anal. Appl., 24:3 (1990), 222–224  mathnet  crossref  mathscinet  zmath  isi
    20. Elmar Schrohe, “Spectral invariance, ellipticity, and the Fredholm property for pseudodifferential operators on weighted Sobolev spaces”, Ann Global Anal Geom, 10:3 (1992), 237  crossref  mathscinet  zmath
    21. V. B. Levenshtam, “Averaging of quasilinear parabolic equations with rapidly oscillating principal part. Exponential dichotomy”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 95–132  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    22. V. B. Levenshtam, “Unique Solvability of Parabolic Equations with Almost-Periodic Coefficients in Hölder Spaces”, Math. Notes, 73:6 (2003), 813–828  mathnet  crossref  crossref  mathscinet  zmath  isi
    23. Simon N. Chandler-Wilde, Marko Lindner, “Sufficiency of Favard's condition for a class of band-dominated operators on the axis”, Journal of Functional Analysis, 254:4 (2008), 1146  crossref
    24. Tomás Caraballo, David Cheban, “Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. I”, Journal of Differential Equations, 246:1 (2009), 108  crossref
    25. Andrea Braides, Giuseppe Riey, Margherita Solci, “Homogenization of Penrose tilings”, Comptes Rendus Mathematique, 347:11-12 (2009), 697  crossref
    26. Simon N. Chandler-Wilde, Johannes Elschner, “Variational Approach in Weighted Sobolev Spaces to Scattering by Unbounded Rough Surfaces”, SIAM J Math Anal, 42:6 (2010), 2554  crossref
    27. Laurent Demanet, Lexing Ying, “Discrete Symbol Calculus”, SIAM Rev, 53:1 (2011), 71  crossref
    28. Alessandro Oliaro, Luigi Rodino, Patrik Wahlberg, “Almost periodic pseudodifferential operators and Gevrey classes”, Annali di Matematica, 2011  crossref
    29. Laurent Demanet, Pierre-David Létourneau, Nicolas Boumal, Henri Calandra, Jiawei Chiu, Stanley Snelson, “Matrix probing: A randomized preconditioner for the wave-equation Hessian”, Applied and Computational Harmonic Analysis, 2011  crossref
    30. Patrik Wahlberg, “Representations of almost periodic pseudodifferential operators and applications in spectral theory”, J. Pseudo-Differ. Oper. Appl, 2011  crossref
    31. Theory Probab. Appl., 56:1 (2012), 1–20  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    32. Chandler-Wilde S.N., Lindner M., “Limit Operators, Collective Compactness, and the Spectral Theory of Infinite Matrices”, Mem. Am. Math. Soc., 210:989 (2011), 1+  crossref  isi
    33. Leonid Parnovski, Roman Shterenberg, “Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic Schrödinger operators”, Ann. Math, 176:2 (2012), 1039  crossref
    34. Sergey Morozov, Leonid Parnovski, Roman Shterenberg, “Complete Asymptotic Expansion of the Integrated Density of States of Multidimensional Almost-Periodic Pseudo-Differential Operators”, Ann. Henri Poincaré, 2013  crossref
    35. Desheng Ji, Chuanyi Zhang, “Pseudo almost periodic weak solutions of a semilinear elliptic equation”, Adv Diff Equ, 2014:1 (2014), 46  crossref
    36. V. E. Slyusarchuk, “The study of nonlinear almost periodic differential equations without recourse to the $\mathscr H$-classes of these equations”, Sb. Math., 205:6 (2014), 892–911  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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