EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 5 / No 4 (2010) Math. Model. Nat. Phenom., 5 4 (2010) 32-53 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
Page(s) 32 - 53
DOI https://doi.org/10.1051/mmnp/20105402
Published online 12 May 2010
  1. M. Sh. Birman. The discrete spectrum of the periodic Schrödinger operator perturbed by a decreasing potential. (Russian) Algebra i Analiz 8 (1996), no. 1, 3–20; English transl., St. Petersburg Math. J. 8 (1997), no. 1, 1–14. [Google Scholar]
  2. M. Reed, B. Simon. Methods of modern mathematical physics. IV: Analysis of operators. Academic Press, New York, 1978. [Google Scholar]
  3. M. M. Skriganov. Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators. (Russian) Trudy Mat. Inst. Steklov, vol. 171, 1985, 171 pp. English transl., Proc. Steklov Inst. Math., 1987, no. 2, 121 pp. [Google Scholar]
  4. M. Sh. Birman. The discrete spectrum in gaps of the perturbed periodic Schrödinger operator. I. Regular perturbations. Boundary value problems, Schrödinger operators, deformation quantization, pp. 334–352, Math. Top., 8, Akademie Verlag, Berlin, 1995. [Google Scholar]
  5. M. Sh. Birman, G. E. Karadzhov, M. Z. Solomyak. Boundedness conditions and spectrum estimates for the operators b(X)a(D) and their analogs. Estimates and asymptotics for discrete spectra of integral and differential equations. Adv. Soviet Math., vol. 7, Amer. Math. Soc., Providence, RI, 1991, pp. 85–106. [Google Scholar]
  6. M. Sh. Birman. Discrete spectrum in the gaps of a continuous one for perturbation with large coupling constant. Estimates and asymptotics for discrete spectra of integral and differential equations. Adv. Soviet Math., vol. 7, Amer. Math. Soc., Providence, RI, 1991, pp. 57–73. [Google Scholar]
  7. S. Alama, P. A. Deift, R. Hempel. Eigenvalue branches of the Schrödinger operator H − λW in a gap of σ(H). Commun. Math. Phys. 121 (1989), 291-321. [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Sh. Birman. Discrete spectrum of the periodic Schrödinger operator for non–negative perturbations. Mathematical results in quantum mechanics (Blossin, 1993), 3–7. Oper. Theory Adv. Appl., Vol. 70, Birkhäuser, Basel, 1994. [Google Scholar]
  9. M. Sh. Birman, M. Z. Solomyak. Spectral theory of selfadjoint operators in Hilbert space. D. Reidel Publishing Company, 1987, Dordrecht, Holland. [Google Scholar]
  10. M. Sh. Birman, M. Z. Solomyak. Estimates for the singular numbers of integral operators. (Russian) Uspekhi Mat. Nauk 32 (1977), no. 1 (193), 17–84. English transl., Russian Math. Surveys 32, no. 1 (1977), 15–89. [Google Scholar]
  11. M. Sh. Birman, M. Z. Solomyak. Compact operators with power-like asymptotics of singular numbers. (Russian) Investigations on linear operators and the theory of functions, 12. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 126 (1983), 21–30. English transl., J. Soviet Math. 27 (1984), 2442–2447. [Google Scholar]
  12. V. A. Sloushch. Generalizations of the Cwikel estimate for integral operators. (Russian) Trudy Sankt-Peterburgskogo mat. obshchestva, vol. 14 (2008), 169-196. English transl., Proc. St. Petersburg Math. Soc., vol. XIV, Amer. Math. Soc. Transl. (2), vol. 228, 2009. [Google Scholar]
  13. M. Sh. Birman, M. Z. Solomyak. Negative discrete spectrum of the Schrödinger operator with large coupling constant: a qualitative discussion. Order, disorder, and chaos in quantum systems (Dubna, 1989). Oper. Theory Adv. Appl., vol. 46, Birkhäuser, Basel, 1990, pp. 3-16. [Google Scholar]
  14. M. Sh. Birman, M. Z. Solomyak. Asymptotic behavior of the spectrum of pseudodifferential operators with anisotropically homogeneous symbols. (Russian) Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 13, no. 3 (1977), 13–21. English transl., Vestnik Leningrad Univ. Math. 10 (1982), 237–247. [Google Scholar]
  15. M. Sh. Birman, M. Z. Solomyak. Asymptotic behavior of the spectrum of pseudodifferential operators with anisotropically homogeneous symbols. II. (Russian) Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 13, no. 3 (1979), 5–10. English transl., Vestnik Leningrad Univ. Math. 12 (1980), 155–161. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.