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List of Research Contributions of Victor Ivrii

Refereed journal publications

  1. (with M. Bronstein) Sharp Spectral Asymptotics for Operators with Irregular Coefficients. Pushing the Limits (final version as of Sep. 2002). Comm. Part. Diff. Equats., v. 28, no 1&2, pp. 99-123, (2003)
  2. Sharp Spectral Asymptotics for Operators with Irregular Coefficients. Pushing the Limits II (final version as of Sep. 2002). Comm. Part. Diff. Equats., v. 28, no 1&2 pp. 125-156, (2003)
  3. Heavy atoms in a superstrong magnetic field, Differential operators and spectral theory, 125-137, Amer. Math. Soc. Transl. Ser. 2, 189, Amer. Math. Soc., Providence, RI, 1999.
  4. Eigenvalue asymptotics for Neumann Laplacian in domains with ultra-thin cusps, Seminaire: Equations aux Derivees Partielles, 1998-1999, Exp. No. X, 8 pp., Semin. Equ. Deriv. Partielles, Ecole Polytech., Palaiseau, 1999.
  5. Precise spectral asymptotics for Neumann Laplacian in domains with cusps, Appl. Anal. 71 (1999), no. 1--4, 139-147.
  6. Accurate spectral asymptotics for periodic operators}, Journees "Equations aux Derivees Partielles" (Saint--Jean--de--Monts, 1999), Exp. No. V, 11 pp., Univ. Nantes, Nantes, 1999.
  7. Asymptotics of the ground state energy of heavy molecules in the strong magnetic field. II. Russian Journal of Math. Phys, 5, (1997), N 3, 321-354.
  8. Heavy molecules in the strong the strong magnetic field. Russian Journal of Math. Phys., 4, (1996), N 4, 449-456.
  9. Asymptotics of the ground state energy of heavy molecules in the strong magnetic field. I, Russian Journal of Math. Phys., 4, (1996), N 1, 29-74.
  10. (with I.M.Sigal) Asymptotics of the ground state energies of large Coulomb systems. Annals of Mathematics, 138, (1993), 243-335.
  11. Eigenvalue asymptotics for two-dimensional Dirac operator with strong magnetic field. Dokl. AN SSSR, 311, (1990), N 5, 1102-1105
  12. Sharp spectral asymptotics for the two-dimensional Schrödinger operator with a strong magnetic field. Dokl. AN SSSR, 306, (1989), N1, 31-34.
  13. Precise spectral asymptotics for Dirac operator with the strong magnetic field. Dokl. AN SSSR, 310, (1989), N 4, 788-792.
  14. Linear hyperbolic equations. Sovremennye problemy matematiki. Fundamental'nye napravleniya. VINITI (Moscow), 33, (1988), 157-247.
  15. Precise spectral asymptotics for elliptic operators on manifolds with boundary. Sibirsk. Mat. Zhurn., 28, (1987), N 1, 107-114.
  16. Bounds for the number of negative eigenvalues of the Schrödinger operator with the strong magnetic field. Dokl. AN SSSR, 297, (1987), N 5, 1043-1046.
  17. Estimates for the spectrum of Dirac operator. Dokl. AN SSSR, 297, (1987), N 6, 1298-1302.
  18. (with L.R.Volevich) Hyperbolic equations. Comments in I.G.Petrovskii. Selected works, Nauka, Moscow, 1986.
  19. Precise spectral asymptotics for elliptic operators on manifolds with boundary. Sibirsk. Mat. Zhurn., 28, (1987), N 1, 107-114.
  20. (with S.I.Fedorova) Dilatations and the asymptotics of the eigenvalues of spectral problems with singularities. Functsional. Anal. i Prilozhen., 20, (1986), N 4, 29-34.
  21. Weyl's asymptotic formula for the Laplace-Beltrami operator in Riemann polyhedra and in domains with conical singularities of the boundary. Dokl. AN SSSR, 288, (1986), N 1, 35-38.
  22. Propagation of singularities of solutions of dissipative boundary value problems for symmetric hyperbolic systems. Dokl. AN SSSR, 287, (1986), N 6, 1299-1301.
  23. Estimations pour le nombre de valeurs propres negatives de l'operateurs de Schrödinger avec potentiels singuliesrs et application au comportement asymptotique des valeurs propres s'accumulant vers -0, aux asymptotiques a deux parameters et a densite des etats. C.R.A.S. Paris, ser 1, 302, (1986), N 15, 535-538.
  24. Estimations pour le nombre de valeurs propres negatives de l'operateurs de Schrödinger avec potentiels singuliesrs et application au comportement asymptotique des grandes valeurs propres. C.R.A.S. Paris, ser 1, 302, (1986), N 14, 491-494.
  25. Estimations pour le nombre de valeurs propres negatives de l'operateurs de Schrödinger avec potentiels singuliesrs.1. C.R.A.S. Paris, ser 1, 302, (1986), N 13, 467-470.
  26. (with O.V.Zaitseva) Strict and nonstrict inequalities in conditions for well-posedness of the Cauchy problem. Uspehi Mat. Nauk, 40, (1985), N 2, 179-180.
  27. Asymptotic of the discrete specrum for some oerators in Rd. Functsional. Anal. i Prilozhen., 19, (1985), N 1, 73-74.
  28. Exact classical and quasiclassical asymptotic behavior of eigenvalues for spectral problems on manifolds with boundary. Dokl. AN SSSR, 277, (1984), N 6, 1307-1310.
  29. The asymptotic behavior of the discrete spectrum of the Schrödinger operator for a system of n particles. Dokl. AN SSSR, 277, (1984), N 4, 785-788.
  30. Precise spectral asymptotics for elliptic operators. Lect. Notes Math., 1100, Springer-Verlag, 1984, v+238pp.
  31. Global and partially global operators. Propagation of singularities and spectral asymptotics. Microlocal Anal. Boulder, Colorado, 1983. Contemp. Math., 27, AMS, 1984, 119-125.
  32. Sharp quasiclassical spectral asymptotics for h-pseudo-differential operators acting in bundles. Imbedding Theorems and their Appl. Trudy Semin. S.L.Soboleva, Nauka, Sibirsk. Dept., (1983), N 1, 30-54.
  33. On precise asymptotics of the eigenvalues for two classes of differential operators in Rn Dokl. AN SSSR, 276, (1984), N 2, 268-270.
  34. The asymptotics of a spectral problem associated to the Laplace- Beltrami operator on a manifold with boundary. Functsional. Anal. i Prilozhen., 17, (1983), N 1, 71-72.
  35. (with O.V.Zaitseva) Correctness of the Cauchy problem for some hyperbolic operators with characteristics of high variable multiplicity. Uspehi Mat. Nauk, 37, (1982), N 3, 187-188.
  36. Exact spectral asymptotics for elliptic operators acting in vector bundles. Functsional. Anal. i Prilozhen., 16, (1982), N 2, 30-38.
  37. Quasiclassical spectral asymptotics for the Schrödinger operator on manifolds with boundary and for h-pseudodifferential operators acting in vector bundles. Dokl. AN SSSR, 263, (1982), N 1, 14-18.
  38. On the asymptotic behavior of eigenvalues for a class of elliptic operators acting in fiber bundles over a manifold with a boundary. Dokl. AN SSSR, 263, (1982), N 3, 530-531.
  39. (with M.A.Shubin) On the asymptotic behavior of the spectral shift function. Dokl. AN SSSR, 263, (1982), N 2, 283-284.
  40. Propagation of singularities of solutions of nonclassical boundary value problems for second-order hyperbolic equations. Trudy Moskov. Mat. Obshch., 43, (1981), 81-91.
  41. Exact spectral asymptotics for the Laplace-Beltrami operator under general elliptic boundary conditions. Functsional. Anal. i Prilozhen., 15, (1981), N 1, 74-75.
  42. The asymptotic behaviour of eigenvalues for some elliptic operators acting in vector bundles over a manifold with boundary. Dokl. AN SSSR, 258, (1981), N 5, 1045-1046.
  43. Wave fronts of solutions of boundary value problems for a class of symmetric hyperbolic systems. Sibirsk. Mat. Zhurn., 21, (1980), N 4, 62-71.
  44. Wave fronts of solutions of boundary value problems for symmetric hyperbolic systems.III. Systems with characteristics of variable multiplicity. Sibirsk. Mat. Zhurn., 21, (1980), N 1, 74-81.
  45. The second term of the spectral asymptotics for the Laplace-Beltrami operator on manifolds with boundary. Functsional. Anal. i Prilozhen., 14, (1980), N 2, 25-34.
  46. The second term of the spectral asymptotics for the Laplace-Beltrami operator on manifolds with boundary and for ellitic operators acting in vector bundles. Dokl. AN SSSR, 250, (1980), N 6, 1300-1302.
  47. Wave fronts of solutions of certain hyperbolic pseudodifferential equations. Trudy Moskov. Mat. Obshch., 39, (1979), 83-112.
  48. Wave fronts of solutions of certain pseudodifferential equations. Trudy Moskov. Mat. Obshch., 39, (1979), 49-82.
  49. Wave fronts of solutions of boundary value problems for symmetric hyperbolic systems.II. Systems with characteristics of constant multiplicity. Sibirsk. Mat. Zhurn., 20, (1979), N 5, 1022-1038.
  50. Wave fronts of solutions of boundary value problems for symmetric hyperbolic systems.I. The fundamental theorem. Sibirsk. Mat. Zhurn., 20, (1979), N 4, 744-751.
  51. Wave fronts of solutions of symmetric pseudodifferential systems. Sibirsk. Mat. Zhurn., 20, (1979), N 3, 557-578.
  52. Propagation of the singularities of the solutions of nonclassical boundary value problems for a wave equation. Funktsional. Anal. i Prilozhen., 13, (1979), N 3, 85-86.
  53. Nonclassical propagation of singularities of a wave equation near the boundary. Dokl. AN SSSR, 241, (1978), N 5, 1013-1015.
  54. Propagation of the singularities of the solutions of a wave equation in a domain which contains corner points. Dokl. AN SSSR, 241, (1978), N 3, 536-539.
  55. Correctness in Gevrey classes of the Cauchy problem for certain non-strictly hyperbolic operators. Izv. Vyssh. Uchebn. Zaved. Matematika, (1978), N 2, 26-35.
  56. Propagation of singularities of solutions of the wave equation near the boundary. Dokl. AN SSSR, 239, (1978), N 4, 772-774.
  57. Propagation of singularities of solutions of the wave equation along the boundary of the domain. Uspehi Mat. Nauk, 32, (1977), N 5, 185-186.
  58. Correctness of the Cauchy problem for nonstrictly hyperbolic operators. III. Trudy Moskov. Mat. Obshch, 34, (1977), 151-170.
  59. Wave fronts of the solutions of boundary value problems for symmetric pseudodifferential systems. Dokl. AN SSSR, 235, (1977), N 5, 1013-1016.
  60. Wave fronts of the solutions of symmetric pseudodifferential systems. Dokl. AN SSSR, 233, (1977), N 6, 1035-1078.
  61. Wave fronts of the solutions of the system that describes crystal optics. Dokl. AN SSSR, 232, (1977), N 4, 763-765.
  62. Conditions for the correctness in Gevrey classes of the Cauchy problem for hyperbolic operators with charateristics of variable multiplicity. Sibirsk. Mat. Zhurn., 17, (1976), N 6, 1256-1270.
  63. Conditions for the correctness in Gevrey classes of the Cauchy problem for non-strictly hyperbolic operators. Sibirsk. Mat. Zhurn., 17, (1976), N 3, 547-563.
  64. Wave fronts of the solutions of certain pseudodifferential equations. Functsional. Anal. i Prilozhen., 10, (1976), N 2, 71-72.
  65. Wave fronts of the solutions of certain hyperbolic pseudodifferential equations. Dokl. AN SSSR, 229, (1976), N 2, 280-283.
  66. Wave fronts of the solutions of certain hyperbolic pseudodifferential equations, and conical refraction. Dokl. AN SSSR, 226, (1976), N 6, 1257-1259.
  67. Wave fronts of the solutions of certain microlocally hyperbolic pseudodifferential equations. Dokl. AN SSSR, 226, (1976), N 5, 1009-1011.
  68. The energy integral for non-strictly hyperbolic operators. Uspehi Mat. Nauk, 30, (1975), N 6, 169-170.
  69. Correctness in in Gevrey classes of the Cauchy problem for non-strictly hyperbolic operators. Uspehi Mat. Nauk, 30, (1975), N 5, 209-210.
  70. Sufficient conditions for regular and completely regular hyperbolicity. Trudy Moskov. Mat. Obsc, 33, (1975), 3-65.
  71. Well-posedness in Gevrey classes of the Cauchy problem for non-strictly hyperbolic operators. Mat. Sbornik, 96, (1975), 390-413.
  72. Correctness in projective Gevrey classes of the Cauchy problem for non-strictly hyperbolic operators with charateristics of variable multiplicity. Dokl. AN SSSR, 222, (1975), N 1, 26-28.
  73. Conditions for the correctness in Gevrey classes of the Cauchy problem for hyperbolic operators with charateristics of variable multiplicity. Dokl. AN SSSR, 221, (1975), N 6, 1253-1255.
  74. Conditions for the correctness in in Gevrey classes of the Cauchy problem for non-strictly hyperbolic operators. Dokl. AN SSSR, 221, (1975), N 4, 775-777.
  75. (with V.M.Petkov) Necessary conditions for the correctness of the Cauchy problem for non-strictly hyperbolic equations. Uspehi Mat. Nauk, 29, (1974), N 5, 3-70.
  76. A certain class of non-strictly hyperbolic operators. Differentsial'nye Uravneniya, 9, (1973), 299-306.
  77. The Cauchy problem for non-strictly hyperbolic equations. Dokl. AN SSSR, 207, (1972), 1032-1034.
  78. The Cauchy problem for non-strictly hyperbolic equations with smooth roots. Dokl. AN SSSR, 204, (1972), 1303-1304.
  79. The Cauchy problem for non-strictly hyperbolic second-order equations. Dokl. AN SSSR, 201, (1971), 778-781.
  80. Differential equations, with multiple characteristics, that have no solution. Dokl. AN SSSR, 198, (1971), 279-282.
  81. The Cauchy problem for non-strictly hyperbolic equations. Dokl. AN SSSR, 197, 517-519.
  82. Exponential decay of the solution of the wave equation in the exterior of an almost star-shaped region. Dokl. AN SSSR, 189 (1969), 938- 940.

Publications in conference proceedings (non-complete list)

  1. Asymptotics of the ground state energy of heavy molecules in the strong magnetic field, IMA, Minneapolis, May 1995 (to appear in Quasiclassical Methods, Springer-Verlag)
  2. Semiclassical spectral asymptotics and multiparticle quantum theory. Proc. Intern. Conf. in PDE and Math. Phys., Holzhau, July 1994; v. 78 (Birkh\"auser), 199-212.
  3. Around Scott correction term(s). Journees "Equat. aux Deriv. Part.", Saint Jean de Monts, 1994.
  4. Semiclassical asymptotics for exchange energy Sem. Equat. aux Deriv. Part., Ecole Polytechnique, 1993-1994, Exp XX, 10pp.
  5. Spectral asymptotics for the family of commuting operators. Intern. Symp. on Operator Calculus and Spectral Theory, Lambrecht, Dec. 1991. Operator Theory, Adv. Appl., v.57, Birkhauser, 1992, 139-148.
  6. Conjoint spectral asymptotics for the families of commuting operators and for operators with the periodic Hamiltonian flow. Sem. Equat. aux Deriv. Part., Ecole Polytechnique, 1991-1992, Exp XV, 11pp.
  7. Semiclassical spectral asymptotics. Summer School on Semiclassical Analysis, Nantes, June 1991. Asterisque, 207 (1992), 7-35.
  8. Eigenvalue asymptotics for Schrödinger operator with constant magnetic field and with decreasing electric potential. Journees "Equat. aux Deriv. Part.", Saint Jean de Monts, 1991.
  9. Non Weylian spectral asymptotics with accurate remainder estimates. Sem. Equat. aux Deriv. Part., Ecole Polytechnique, 1990-1991, Exp. V, 10pp.
  10. Spectral asymptotics with highly accurate remainder estimates. Sem. Equat. aux Deriv. Part., Ecole Polytechnique, 1989-1990, Exp. VI, 16pp.
  11. (with A.Kachalkina) Spectral asymptotics with highly accurate remainder estimates. Order, Disorder and Chaos in Quantum Systems. Proc. Conf. Dubna, Oct.1989, Operator Theory: Advances and Appl., 46, Birkhauser, 1990, 61-63.
  12. (with E.Filippov, A.Kachalkina) Spectral asymptotics with highly accurate remainder estimates. Intern. Conf. Integral Equat. and Inverse Problem. Varna, Sept. 1989, Pitman Res. Notes in Math. Sci., Longman Sci.& Tech., 1991, 146--153.
  13. Spectral asymptotics for Schrödinger and Dirac operators with strong magnetic field. Schrödinger operators. Proc. Conf., Dubna, Oct. 1988, Word Sci. Press, 1990.
  14. Estimates for a number of negative eigenvalues of the Schrödinger operator with intensive magnetic field. Journees "Equat. aux Deriv. Part.", Saint Jean de Monts, 1987. Exp. XX, 7pp.
  15. Estimates for a number of negative eigenvalues of the Schrödinger operator with singular potentials. Proc. of the Intern. Congress of Mathematicians, Berkeley, 1986, 1084-1093.
  16. (with S.Fedorova) Asymptotics of of the eigenvalues of spectral problems with singularities. Differ. Eqs. and appl. I, II. Proc. Conf. Ruse (Bulg.), 1985., Tech. Univ. Ruse, 1987, 163-166.
  17. Propagation of singularities of solutions of symmetric hyperbolic systems. Proc. of the Intern. Congress of Mathematicians, Helsinki, 1978, (1980), 771-776.
  18. Propagation of singularities of solutions of symmetric hyperbolic systems. Partial Diff. Eq. Proc. Conf. Novosibirsk, 1978, Nauka, Sibirsk. Otdel., (1979), 122-128.
  19. Wave fronts of solutions of some pseudodifferential equations. Proc. of All-Union Conf. in Partial Diff. Eq., Moscow State Univ. 1976, MGU (1978), 117-119.
  20. Cauchy problem for non-strictly hyperbolic equations. Applications of functional methods to the boundary value problems of math. physics. Proc. third Soviet-Czechoslovak Conf., Novosibirsk, 1971, 82-89.

Preprints

  1. Heavy molecules in the strong magnetic field. Estimates for ionization energy and excessive charge. (40 pp) Submitted in Russian Journal of Math. Phys.
  2. Asymptotics of the ground state energy of heavy molecules in the very strong magnetic field. (in progress).
  3. Semiclassical microlocal analysis and precise spectral asymptotics. Chapter 12. Preprint 9. Ecole Polytechnique, Preprint. Centre Math., Preprint N 1041, July 1992, 101pp.
  4. Semiclassical microlocal analysis and precise spectral asymptotics. Chapter 11. Preprint 8. Ecole Polytechnique, Preprint. Centre Math., Preprint N 1037, May 1992, 102pp.
  5. Semiclassical microlocal analysis and precise spectral asymptotics. Chapter 10. Preprint 7. Ecole Polytechnique. Centre Math., Preprint N 1031, March 1992, 150pp.
  6. Semiclassical microlocal analysis and precise spectral asymptotics. Chapters 8, 9. Preprint 6. Ecole Polytechnique, Centre Math., Preprint M1018.1091, Oct. 1991, 81pp.
  7. Semiclassical microlocal analysis and precise spectral asymptotics. Chapter 7. Preprint 5. Ecole Polytechnique, Centre Math., Preprint M980.0691, June 1991, 85pp.
  8. Semiclassical microlocal analysis and precise spectral asymptotics. Chapter 6. Preprint 4. Ecole Polytechnique, Centre Math., Preprint M 974.0591, May 1991, 120pp.
  9. Semiclassical microlocal analysis and precise spectral asymptotics. Chapter 5. Preprint 3. Ecole Polytechnique, Centre Math., Preprint M971.0291, February 1991, 80pp.
  10. Semiclassical microlocal analysis and precise spectral asymptotics. Chapter 4. Preprint 2. Ecole Polytechnique, Centre Math., Preprint M969.0191, January 1991, 107pp.
  11. Semiclassical microlocal analysis and precise spectral asymptotics. Chapters 1-3. Preprint 1. Ecole Polytechnique, Centre Math., Preprint M964.1190, November 1990, 146pp.
  12. Precise semi-classical spectral asymptotics for elliptic operators on manifolds with boundary. Preprint Deposed VINITI, 1987.

Other publications

Working in Magnitogorsk Mining-Metallurgical Institute I published few tiny problem-brochures containing personalized home-works for students (which means that each problem had 30 variants): method of characteristics, Fourier method, integral transformations, variational methods, Green functions, self-similar solutions. All of them gone beyound recovery.