List of Alexander Pushnitski's publications

  1. S. N. Naboko, A. B. Pushnitski,
    Point spectrum on a continuous spectrum for weakly perturbed Stark type operators
    Functional analysis and its applications, 29, no. 4 (1995), 248-257.
    DOI: 10.1007/BF01077472

  2. E. L. Korotyaev, A. B. Pushnitski,
    Scattering by anisotropic potential in a constant electric field (in Russian),
    Zap. Nauchn. Seminarov POMI, 230 (1995), 103-114.
    English translation in: J. Math. Sci. (New York) 91, no. 2 (1998), 2768--2775.
    DOI: 10.1007/BF02433992

  3. S. N. Naboko, A. B. Pushnitski,
    On the embedded eigenvalues and dense point spectrum of the Stark-like Hamiltonians,
    Math. Nachr.183 (1997), 185-200.
    DOI: 10.1002/mana.19971830112

  4. A. B. Pushnitski,
    The spectrum of Liouville operators and multiparticle Hamiltonians associated to one-particle Hamiltonians with singular continuous spectrum,
    J. Math. Phys. 38, no. 5 (1997), 2266-2273.
    DOI: 10.1063/1.531972

  5. M. I. Belishev, A. B. Pushnitski,
    On a triangular factorization of positive operators (in Russian),
    Zap. Nauchn. Seminarov POMI, 239 (1997), 45-60.
    English translation in: J. Math. Sci. (New York) 96, no. 4 (1999), 3312--3320.
    DOI: 10.1007/BF02172806

  6. M. Sh. Birman, A. B. Pushnitski,
    Discrete spectrum in the gaps of the perturbed pseudorelativistic magnetic Hamiltonian (in Russian),
    Zap. Nauchn. Seminarov POMI, 249 (1997), 102-117.
    English translation in J. Math. Sci. (New York) 101 (2000), no. 5, 3437--3447.
    DOI: 10.1007/BF02680144
    Click here for the text of the paper in Russian

  7. A. B. Pushnitski,
    Representation for the spectral shift function for perturbations of a definite sign,
    St.Petersburg Math. J. 9, no. 6 (1998), 1181-1194.

  8. M. Sh. Birman, A. B. Pushnitski,
    Spectral shift function, amazing and multifaceted,
    Integr. Equ. Oper. Theory 30, no. 2 (1998), 191-199.

    DOI: 10.1007/BF01238218

  9. A. B. Pushnitski,
    Integral estimates for the spectral shift function,
    St.Petersburg Math. J. 10, no. 6 (1999), 1047-1070.

  10. A. B. Pushnitski,
    Estimates for the spectral shift function of the polyharmonic operator,
    J. Math. Phys. 40, no. 11 (1999), 5578-5592.
    DOI: 10.1063/1.533047

  11. A. B. Pushnitski,
    Spectral shift function of the Schrodinger operator in the large coupling constant limit,
    Comm. in PDE 25, no 3&4 (2000), 703-736.
    DOI: 10.1080/03605300008821528

  12. A. B. Pushnitski,
    The spectral shift function and the invariance principle,
    J. Functional Analysis, 183, no.2 (2001), 269-320.
    DOI: 10.1006/jfan.2001.3751

  13. A. Pushnitski, M. Ruzhansky,
    Spectral shift function of the Schrodinger operator in the large coupling constant limit, II. Positive perturbations.
    Comm. in PDE, 27, no.7 & 8 (2002), 1373-1405.
    DOI: 10.1081/PDE-120005842

  14. A. Pushnitski, M. Ruzhansky,
    Spectral shift function of the Schrodinger operator in the large coupling constant limit,
    Functional Analysis and Its Applications, 36, no. 3 (2002), 250-252.
    DOI: 10.1023/A:1020170626399

  15. E. Korotyaev, A. Pushnitski,
    Trace formulae and high energy asymptotics for Stark operator,
    Comm. in PDE 28, no.3 & 4 (2003), 817-842.
    DOI: 10.1081/PDE-120020498

  16. E. Korotyaev, A. Pushnitski,
    On the high energy asymptotics of the integrated density of states,
    Bull. London Math. Soc. 35, no.6, 770-776 (2003).
    DOI: 10.1112/S0024609303002467

  17. E. Korotyaev, A. Pushnitski,
    A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian,
    J. Funct. Anal. 217, 221-248 (2004).
    DOI: 10.1016/j.jfa.2004.03.003

  18. V. Bruneau, A. Pushnitski, G. Raikov,
    Spectral Shift Function in Strong Magnetic Fields,
    St. Petersburg Math. J. 16, no. 1, 207-238 (2005).

  19. A.Pushnitski, I. Sorrell,
    High energy asymptotics and trace formulas for the perturbed harmonic oscillator,
    Ann. Henri Poincare, 7, no. 2, 381-396 (2006).
    DOI: 10.1007/s00023-005-0253-5

  20. N. Filonov, A. Pushnitski,
    Spectral asymptotics of Pauli operators and orthogonal polynomials in complex domains,
    Comm. Math. Phys. 264 (2006), no. 3, 759-772.

    DOI: 10.1007/s00220-006-1520-0

  21. A. Pushnitski, V. Sloushch,
    Spectral shift function for the Stark operator in the large coupling constant limit,
    Asymptotic Analysis 51, no. 1, 63-89 (2007).

  22. A. Pushnitski, G. Rozenblum,
    Eigenvalue clusters of the Landau Hamiltonian in the exterior of a compact domain,
    Documenta Math. 12, 569-586 (2007).


  23. A. Pushnitski,
    The scattering matrix and the differences of spectral projections,
    Bulletin London Math. Soc. 40, 227-238 (2008).

  24. F. Gesztesy, A. Pushnitski, B. Simon,
    On the Koplienko spectral shift function, I. Basics
    Journal of Mathematical Physics, Analysis, Geometry 4 (2008), no. 1, 63-107

  25. D. Damanik, A. Pushnitski, B. Simon,
    The analytic theory of matrix orthogonal polynomials,
    Surveys in Approximation Theory 4, 1-85 (2008).

  26. A. Pushnitski,
    The spectral flow, the Fredholm index, and the spectral shift function,
    in: Spectral Theory of Differential Operators: M.Sh.Birman 80th Anniversary Collection, AMS Translations (2), Advances in Mathematical Sciences, 225, 141-155 (2008).

  27. A. Pushnitski,
    Operator theoretic methods for the eigenvalue counting function in spectral gaps,
    Ann. Henri Poincare 10, 793-822 (2009).
    DOI: 10.1007/s00023-009-0422-z

  28. V. Buslaev, A. Pushnitski,
    The scattering matrix and associated formulas in Hamiltonian mechanics,
    Comm. Math. Phys. 293, no.2, 563-588 (2010).
    DOI: 10.1007/s00220-009-0937-7

  29. A. Pushnitski and D. Yafaev,
    Spectral theory of discontinuous functions of self-adjoint operators and scattering theory,
    J. Funct. Anal. 259, no. 8, 1950-1973 (2010).
    DOI: 10.1016/j.jfa.2010.07.001

  30. A. Pushnitski,
    Spectral theory of discontinuous functions of self-adjoint operators: essential spectrum
    Integr. Equ. Oper. Theory, 68, 75-99 (2010).
    DOI: 10.1007/s00020-010-1789-4

  31. A. Pushnitski,
    The Birman-Schwinger principle on the essential spectrum,
    J. Functional Analysis, 261, 2053-2081 (2011).
    DOI: 10.1016/j.jfa.2011.06.002

  32. A. Pushnitski, G. Rozenblum,
    On the spectrum of Bargmann-Toeplitz operators with symbols of a variable sign,
    Journal d'Analyse Mathematique, 114, no. 1, 317-340 (2011).
    DOI: 10.1007/s11854-011-0019-6

  33. E.B.Davies, A. Pushnitski,
    Non-Weyl Resonance Asymptotics for Quantum Graphs,
    Analysis & PDE, 4 no.5, 729-756 (2011).
    DOI: 10.2140/apde.2011.4.729

  34. A. Pushnitski,
    An integer-valued version of the Birman-Krein formula,
    Functional Analysis and Its Applications, vol. 44, no. 4, 307-312 (2011).
    DOI: 10.1007/s10688-010-0041-y

  35. A. Pushnitski,
    Scattering matrix and functions of self-adjoint operators,
    Journal of Spectral Theory, 1, 221-236 (2011).
    DOI: 10.4171/JST/10

  36. D. Bulger, A. Pushnitski,
    The spectral density of the scattering matrix for high energies,
    Comm. Math. Phys. 316, no.3, 693-704 (2012).

  37. D. Bulger, A. Pushnitski,
    The spectral density of the scattering matrix of the magnetic Schrodinger operator for high energies,
    J. Spectral Theory 3, no. 4, 517-534 (2013).
    DOI: 10.4171/JST/54

  38. A. Pushnitski, G. Raikov, C. Villegas-Blas,
    Asymptotic density of eigenvalue clusters for the perturbed Landau hamiltonian,
    Comm. Math. Phys. 320, no.2, 425-453 (2013).
    DOI: 10.1007/s00220-012-1643-4

  39. A. Pushnitski, D.Yafaev,
    A multichannel scheme in smooth scattering theory,
    J. Spectr. Theory 3, no. 4, 601-634 (2013).
    DOI: 10.4171/JST/58

  40. S. Nakamura, A. Pushnitski,
    The spectrum of the scattering matrix near resonant energies in the semiclassical limit,
    Transactions Amer. Math. Soc. 366, 1725-1747 (2014).

  41. A. Pushnitski, D.Yafaev,
    Spectral theory of piecewise continuous functions of self-adjoint operators,
    Proc. Lond. Math. Soc. (3) 108, no. 5, 1079-1115 (2014).

  42. A. Pushnitski, A.Volberg,
    Scattering theory and Banach space valued singular integrals,
    Int. Math. Res. Notices 2014, no. 20, 5667-5696 (2014).

  43. A. Pushnitski, A.Volberg,
    Spectral perturbation theory and the two weights problem,
    Indiana Univ. Math. J. 63, no. 5, 1349-1364 (2014).

  44. P. Gerard, A. Pushnitski,
    An inverse problem for self-adjoint positive Hankel operators,
    Int. Math. Res. Notices 2015, no. 13, 4505-4535 (2015).

  45. R. Frank, A. Pushnitski,
    Trace class conditions for functions of Schrödinger operators,
    Commun. Math. Physics 335, 477-496 (2015).

  46. A. Pushnitski, D. Yafaev,
    Spectral and scattering theory of self-adjoint Hankel operators with piecewise continuous symbols,
    J. Operator Theory 74, no.2, 417-455 (2015).

  47. R. Frank, A. Pushnitski,
    The spectral density of a product of spectral projections,
    J. Functional Analysis, 268, no. 12, 3867-3894 (2015).

  48. A. Pushnitski,
    The spectral density of a difference of spectral projections,
    Comm. Math. Phys. 338, no. 3, 1153-1181 (2015).

  49. A. Pushnitski, D. Yafaev,
    Sharp estimates for singular values of Hankel operators,
    Integr. Equ. Oper. Theory, 83, no. 3, 393-411 (2015).

  50. A. Pushnitski, D. Yafaev,
    Asymptotic behavior of eigenvalues of Hankel operators,
    Int. Math. Res. Notices 2015, no. 22, 11861-11886 (2015).
    DOI: 10.1093/imrn/rnv048

  51. A. Pushnitski, D. Yafaev,
    Localization principle for compact Hankel operators,
    J. Funct. Anal. 270 (2016), pp. 3591-3621.

  52. A. Pushnitski, D. Yafaev,
    Best rational approximation of functions with logarithmic singularities,
    Constructive Approximation 46 (2017), pp. 243-269.

  53. A. Pushnitski, D. Yafaev,
    Spectral asymptotics for compact self-adjoint Hankel operators,
    Journal of Spectral Theory (special issue dedicated to the memory of Yuri Safarov) 6 (2016), pp. 921-953.
    DOI: 10.4171/JST/148

  54. K.-M. Perfekt, A. Pushnitski,
    On Helson matrices: moment problems, non-negativity, boundedness, and finite rank,
    Proceedings of the London Math. Soc, 116, no. 1 (2018), pp. 101-134.
    DOI: 10.1112/plms.12068

  55. K.-M. Perfekt, A. Pushnitski,
    On the spectrum of the multiplicative Hilbert matrix,
    Arkiv for Mathematik, 56, no.1 (2018), pp. 163-183

  56. E. Fedele, A. Pushnitski,
    Weighted integral Hankel operators with continuous spectrum,
    to appear in Concrete Operators,

  57. N. Miheisi, A. Pushnitski,
    A Helson matrix with explicit eigenvalue asymptotics,
    to appear in J. Funct. Anal,

  58. A. Pushnitski,
    Spectral asymptotics for a class of Toeplitz operators on the Bergman space,
    to appear in proceedings of IWOTA-2017,

  59. P. Gerard, A. Pushnitski,
    Weighted model spaces and Schmidt subspaces of Hankel operators,

  60. P. Gerard, A. Pushnitski,
    Inverse spectral theory for a class of non-compact Hankel operators,
    to appear in Mathematika,