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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 1989, Volume 64, Pages 5–242 (Mi intf170)  

This article is cited in 25 scientific papers (total in 26 papers)

Spectral theory of differential operators

G. V. Rozenblum, M. Z. Solomyak, M. A. Shubin


Full text: PDF file (34478 kB)

Bibliographic databases:

UDC: 517.951+517.954+517.956.227+517.984

Citation: G. V. Rozenblum, M. Z. Solomyak, M. A. Shubin, “Spectral theory of differential operators”, Partial differential equations – 7, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 64, VINITI, Moscow, 1989, 5–242

Citation in format AMSBIB
\Bibitem{RozSolShu89}
\by G.~V.~Rozenblum, M.~Z.~Solomyak, M.~A.~Shubin
\paper Spectral theory of differential operators
\inbook Partial differential equations~--~7
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr.
\yr 1989
\vol 64
\pages 5--242
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intf170}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1033500}
\zmath{https://zbmath.org/?q=an:0715.35057|0805.35081}


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    1. A. I. Karol', “Complex powers of the Schrödinger operator with a homogeneous, degenerate potential”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 61–83  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. K. Kh. Boimatov, “Asymptotics of spectral projectors of pseudodifferential operators”, Funct. Anal. Appl., 26:1 (1992), 42–44  mathnet  crossref  mathscinet  zmath  isi
    3. K. Kh. Boimatov, “Multidimensional Distribution Functions for Elliptic Operators”, Funct. Anal. Appl., 27:4 (1993), 273–275  mathnet  crossref  mathscinet  zmath  isi
    4. D. V. Kosygin, A. A. Minasov, Ya. G. Sinai, “Statistical properties of the spectra of Laplace–Beltrami operators on Liouville surfaces”, Russian Math. Surveys, 48:4 (1993), 1–142  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. S. Z. Levendorskii, “Magnetic Floquet Theory and Spectral Asymptotics for Schrödinger Operators”, Funct. Anal. Appl., 30:4 (1996), 282–285  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. K. Kh. Boimatov, “On the Spectrum of a Self-Adjoint Polynomial Pencil”, Funct. Anal. Appl., 31:3 (1997), 204–207  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. S. I. Boyarchenko, S. Z. Levendorskii, “Spectral Asymptotics of Laplacians on Horns: the Case of a Rapidly Growing Counting Function”, Funct. Anal. Appl., 32:3 (1998), 198–200  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. M. S. Agranovich, “Spectral problems for second-order strongly elliptic systems in smooth and non-smooth domains”, Russian Math. Surveys, 57:5 (2002), 847–920  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. N. V. Artamonov, “Estimates of solutions of certain classes of second-order differential equations in a Hilbert space”, Sb. Math., 194:8 (2003), 1113–1123  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. A. A. Shkalikov, “Spectral Portraits of the Orr–Sommerfeld Operator with Large Reynolds Numbers”, Journal of Mathematical Sciences, 124:6 (2004), 5417–5441  mathnet  crossref  mathscinet  zmath
    11. N. G. Kuznetsov, O. V. Motygin, “The Steklov problem in a half-plane: the dependence of eigenvalues on a piecewise-constant coefficient”, J. Math. Sci. (N. Y.), 127:6 (2005), 2429–2445  mathnet  crossref  mathscinet  zmath
    12. V. R. Fatalov, “Occupation times and exact asymptotics of small deviations of Bessel processes for $L^p$-norms with $p>0$”, Izv. Math., 71:4 (2007), 721–752  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. V. R. Fatalov, “Exact Asymptotics of Small Deviations for a Stationary Ornstein–Uhlenbeck Process and Some Gaussian Diffusion Processes in the $L_p$-Norm, $2\le p\le\infty$”, Problems Inform. Transmission, 44:2 (2008), 138–155  mathnet  crossref  mathscinet  isi  elib
    14. A. A. Shkalikov, “On the basis property of root vectors of a perturbed self-adjoint operator”, Proc. Steklov Inst. Math., 269 (2010), 284–298  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    15. V. M. Kaplitskiǐ, “Asymptotics of the distribution of eigenvalues of a selfadjoint second order hyperbolic differential operator on the two-dimensional torus”, Siberian Math. J., 51:5 (2010), 830–846  mathnet  crossref  mathscinet  isi  elib
    16. M. S. Agranovich, “Spectral problems in Lipschitz domains”, Journal of Mathematical Sciences, 190:1 (2013), 8–33  mathnet  crossref  mathscinet
    17. D. A. Popov, “On the second term in the Weyl formula for the spectrum of the Laplace operator on the two-dimensional torus and the number of integer points in spectral domains”, Izv. Math., 75:5 (2011), 1007–1045  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. M. G. Gadoev, “Spektralnaya asimptotika nesamosopryazhennykh vyrozhdayuschikhsya ellipticheskikh operatorov s singulyarnymi matrichnymi koeffitsientami na otrezke”, Ufimsk. matem. zhurn., 3:3 (2011), 26–54  mathnet  zmath
    19. V. M. Kaplitskii, “On regulariziers of unbounded linear operators in Banach spaces”, J. Math. Sci. (N. Y.), 194:6 (2013), 651–655  mathnet  crossref  mathscinet
    20. V. R. Fatalov, “Ergodic means for large values of $T$ and exact asymptotics of small deviations for a multi-dimensional Wiener process”, Izv. Math., 77:6 (2013), 1224–1259  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    21. M. G. Gadoev, S. A. Iskhokov, “Spectral properties of degenerate elliptic operators with matrix coefficients”, Ufa Math. J., 5:4 (2013), 37–48  mathnet  crossref  elib
    22. R. S. Ismagilov, “Asymptotic form of the spectrum of operators associated with $p$-adic fields”, Theoret. and Math. Phys., 180:1 (2014), 753–758  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    23. A. A. Shkalikov, “Perturbations of self-adjoint and normal operators with discrete spectrum”, Russian Math. Surveys, 71:5 (2016), 907–964  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    24. A. M. Vershik, E. D. Gluskin, V. A. Kozlov, A. A. Laptev, B. M. Makarov, B. S. Mityagin, P. Nevai, G. V. Rozenblum, T. A. Suslina, N. N. Ural'tseva, D. R. Yafaev, “Mikhail Zakharovich Solomyak (obituary)”, Russian Math. Surveys, 72:5 (2017), 955–961  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    25. K. A. Radomirskaya, “Spektralnye i nachalno-kraevye zadachi sopryazheniya”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 63, no. 2, Rossiiskii universitet druzhby narodov, M., 2017, 316–339  mathnet  crossref  mathscinet
    26. G. V. Rozenblyum, “O matematicheskikh rabotakh Mikhaila Zakharovicha Solomyaka”, Algebra i analiz, 30:3 (2018), 3–29  mathnet  elib
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