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,
    Concrete Operators, 4, no.1 (2017), 121-129.

  57. N. Miheisi, A. Pushnitski,
    A Helson matrix with explicit eigenvalue asymptotics,
    J. Funct. Anal, 275, no.4 (2018), 967-987.

  58. A. Pushnitski,
    Spectral asymptotics for a class of Toeplitz operators on the Bergman space,
    Proceedings of IWOTA-2017:
    Oper. Theory Adv. Appl., 268 (2018), 397-412.

  59. P. Gerard, A. Pushnitski,
    Weighted model spaces and Schmidt subspaces of Hankel operators,
    to appear in J. London Math. Soc.

  60. P. Gerard, A. Pushnitski,
    Inverse spectral theory for a class of non-compact Hankel operators,
    Mathematika, 65, no.1 (2019), 132-156.

  61. N. Miheisi, A. Pushnitski,
    Restriction theorems for Hankel operators,
    to appear in Studia Math.

  62. R. Frank, A. Pushnitski,
    Kato smoothness and functions of perturbed self-adjoint operators ,
    to appear in Adv. Math.

  63. R. Frank, A. Pushnitski,
    Schatten class conditions for functions of Schrodinger operators,
    to appear in Annales Henri Poincaré

  64. P. Gerard, A. Pushnitski,
    The structure of Schmidt subspaces of Hankel operators: a short proof,

  65. N. Nikolski, A. Pushnitski,
    Szegő-type limit theorems for "multiplicative Toeplitz" operators and non-Følner approximations,