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Uspekhi Mat. Nauk, 1979, Volume 34, Issue 2(206), Pages 95–135 (Mi umn4044)  

This article is cited in 43 scientific papers (total in 44 papers)

The spectral theory and the index of elliptic operators with almost periodic coefficients

M. A. Shubin

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English version:
Russian Mathematical Surveys, 1979, 34:2, 109–157

Bibliographic databases:

UDC: 517.4
MSC: 35Pxx, 47C15, 47E05, 35B15
Received: 11.07.1976
Revised: 23.01.1978

Citation: M. A. Shubin, “The spectral theory and the index of elliptic operators with almost periodic coefficients”, Uspekhi Mat. Nauk, 34:2(206) (1979), 95–135; Russian Math. Surveys, 34:2 (1979), 109–157

Citation in format AMSBIB
\by M.~A.~Shubin
\paper The spectral theory and the index of elliptic operators with almost periodic coefficients
\jour Uspekhi Mat. Nauk
\yr 1979
\vol 34
\issue 2(206)
\pages 95--135
\jour Russian Math. Surveys
\yr 1979
\vol 34
\issue 2
\pages 109--157

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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. S. M. Kozlov, “The distribution of the eigenvalues of differential operators in large domains”, Russian Math. Surveys, 37:5 (1982), 180–181  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. E. M. Savko, “Analyticity of almost periodic functions with bounded Bloch spectrum”, Funct. Anal. Appl., 16:2 (1982), 147–148  mathnet  crossref  mathscinet  zmath  isi
    5. D. Schenk, M. A. Shubin, “Asymptotic expansion of the state density and the spectral function of a Hill operator”, Math. USSR-Sb., 56:2 (1987), 473–490  mathnet  crossref  mathscinet  zmath
    6. 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
    7. D. Schenk, M. A. Shubin, “Asymptotic expansion of the spectral function of the Hill operator”, Funct. Anal. Appl., 20:1 (1986), 78–79  mathnet  crossref  mathscinet  zmath  isi
    8. Jingbo Xia, “Geometric invariants of the quantum Hall effect”, Comm Math Phys, 119:1 (1988), 29  crossref  mathscinet  zmath  isi
    9. Jingbo Xia, “Spectral convergence of self-adjoint operators and generalized wave operators”, Journal of Functional Analysis, 77:1 (1988), 176  crossref
    10. Jingbo Xia, “The Floquet theory and the state density of quasi-periodic Schrödinger operators”, Journal of Differential Equations, 86:2 (1990), 243  crossref
    11. M. Gromov, M. A. Shubin, “Von Neumann spectra near zero”, GAFA Geom funct anal, 1:4 (1991), 375  crossref  mathscinet  zmath  elib
    12. A. V. Sobolev, “The asymptotic behavior of the discrete spectrum in the gaps of the continuous spectrum of a perturbed hill operator”, Funct. Anal. Appl., 25:2 (1991), 162–164  mathnet  crossref  mathscinet  zmath  isi
    13. Russell Johnson, “Oscillation theory and the density of states for the Schrödinger operator in odd dimension”, Journal of Differential Equations, 92:1 (1991), 145  crossref
    14. J. Bellissard, A. van Elst, H. Schulz- Baldes, “The noncommutative geometry of the quantum Hall effect”, J Math Phys (N Y ), 35:10 (1994), 5373  crossref  mathscinet  zmath  adsnasa  isi
    15. M. A. Shubin, “Discrete Magnetic Laplacian”, Comm Math Phys, 164:2 (1994), 259  crossref  mathscinet  zmath  adsnasa  isi  elib
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    21. A. I. Shtern, “Almost periodic functions and representations in locally convex spaces”, Russian Math. Surveys, 60:3 (2005), 489–557  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    22. M. M. Skriganov, A. V. Sobolev, “On the spectrum of polyharmonic operators with limit-periodic potentials”, St. Petersburg Math. J., 17:5 (2006), 815–833  mathnet  crossref  mathscinet  zmath  elib
    23. Peter D. Hislop, Olivier Lenoble, “Basic properties of the current-current correlation measure for random Schrödinger operators”, J Math Phys (N Y ), 47:11 (2006), 112106  crossref  mathscinet  zmath  isi
    24. A. L. Carey, F. A. Sukochev, “Dixmier traces and some applications in non-commutative geometry”, Russian Math. Surveys, 61:6 (2006), 1039–1099  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    25. Moulay-Tahar Benameur, Thierry Fack, “Type II non-commutative geometry. I. Dixmier trace in von Neumann algebras”, Advances in Mathematics, 199:1 (2006), 29  crossref
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    27. Yulia Karpeshina, Young-Ran Lee, “Spectral properties of polyharmonic operators with limit-periodic potential in dimension two”, J Anal Math, 102:1 (2007), 225  crossref  mathscinet  zmath  isi
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    31. Skripka A., “On properties of the xi-function in semi-finite von Neumann algebras”, Integral Equations Operator Theory, 62:2 (2008), 247–267  crossref  isi
    32. Yu. A. Kordyukov, “Index theory and non-commutative geometry on foliated manifolds”, Russian Math. Surveys, 64:2 (2009), 273–391  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    33. Daniel Lenz, Norbert Peyerimhoff, Olaf Post, Ivan Veselić, “Continuity of the Integrated Density of States on Random Length Metric Graphs”, Math Phys Anal Geom, 2009  crossref  mathscinet  isi
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    35. Patrik Wahlberg, “Representations of almost periodic pseudodifferential operators and applications in spectral theory”, J. Pseudo-Differ. Oper. Appl, 2011  crossref
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