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
   preprint


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.
   preprint


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
   preprint


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


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
    preprint


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
    preprint


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
    preprint


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
    preprint


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
    preprint


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
    preprint


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
    preprint


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
    preprint


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


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
    preprint


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
    preprint


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).
    preprint


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


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


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
    preprint


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


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).
    preprint


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
    preprint


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
    preprint


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
    preprint


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
    preprint


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
    preprint


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
    preprint


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
    preprint


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
    preprint


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


36. D. Bulger, A. Pushnitski,
    The spectral density of the scattering matrix for high energies,
    Comm. Math. Phys. 316, no.3, 693-704 (2012).
    DOI:10.1007/s00220-012-1551-7
    preprint


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
    preprint


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
    preprint


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
    preprint


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).
    DOI:10.1090/S0002-9947-2013-06077-1
    preprint


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).
    DOI:10.1112/plms/pdt049
    preprint


42. A. Pushnitski, A.Volberg,
    Scattering theory and Banach space valued singular integrals,
    Int. Math. Res. Notices 2014, no. 20, 5667-5696 (2014).
    DOI:10.1093/imrn/rnt137
    preprint


43. A. Pushnitski, A.Volberg,
    Spectral perturbation theory and the two weights problem,
    Indiana Univ. Math. J. 63, no. 5, 1349-1364 (2014).
    DOI:10.1512/iumj.2014.63.5389
    preprint


44. P. Gerard, A. Pushnitski,
    An inverse problem for self-adjoint positive Hankel operators,
    Int. Math. Res. Notices 2015, no. 13, 4505-4535 (2015).
    DOI:10.1093/imrn/rnu073
    preprint


45. R. Frank, A. Pushnitski,
    Trace class conditions for functions of Schrödinger operators,
    Commun. Math. Physics 335, 477-496 (2015).
    DOI:0.1007/s00220-014-2205-8
    preprint


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).
    DOI:10.7900/jot.2014aug11.2052
    preprint


47. R. Frank, A. Pushnitski,
    The spectral density of a product of spectral projections,
    J. Functional Analysis, 268, no. 12, 3867-3894 (2015).
    DOI:10.1016/j.jfa.2015.03.018
    preprint


48. A. Pushnitski,
    The spectral density of a difference of spectral projections,
    Comm. Math. Phys. 338, no. 3, 1153-1181 (2015).
    DOI:10.1007/s00220-015-2393-x
    preprint


49. A. Pushnitski, D. Yafaev,
    Sharp estimates for singular values of Hankel operators,
    Integr. Equ. Oper. Theory, 83, no. 3, 393-411 (2015).
    DOI:10.1007/s00020-015-2239-0
    preprint


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
    preprint


51. A. Pushnitski, D. Yafaev,
    Localization principle for compact Hankel operators,
    J. Funct. Anal. 270 (2016), pp. 3591-3621.
    DOI:10.1016/j.jfa.2015.10.018
    preprint


52. A. Pushnitski, D. Yafaev,
    Best rational approximation of functions with logarithmic singularities,
    Constructive Approximation 46 (2017), pp. 243-269.
    DOI:10.1007/s00365-016-9347-1
    preprint


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
    preprint


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
    preprint


55. K.-M. Perfekt, A. Pushnitski,
    On the spectrum of the multiplicative Hilbert matrix,
    Arkiv for Mathematik, 56, no.1 (2018), pp. 163-183
    DOI: http://dx.doi.org/10.4310/ARKIV.2018.v56.n1.a10
    preprint


56. E. Fedele, A. Pushnitski,
    Weighted integral Hankel operators with continuous spectrum,
    Concrete Operators, 4, no.1 (2017), 121-129.
    DOI: http://dx.doi.org/10.1515/conop-2017-0009
    preprint


57. N. Miheisi, A. Pushnitski,
    A Helson matrix with explicit eigenvalue asymptotics,
    J. Funct. Anal, 275, no.4 (2018), 967-987.
    https://doi.org/10.1016/j.jfa.2017.11.002
    preprint


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.
    preprint


59. P. Gerard, A. Pushnitski,
    Inverse spectral theory for a class of non-compact Hankel operators,
    Mathematika, 65, no.1 (2019), 132-156.
    DOI: https://doi.org/10.1112/S0025579318000281
    preprint


60. R. Frank, A. Pushnitski,
    Kato smoothness and functions of perturbed self-adjoint operators ,
    Adv. Math. 351 (2019), 343-387.
    DOI: https://doi.org/10.1016/j.aim.2019.05.002
    preprint


61. R. Frank, A. Pushnitski,
    Schatten class conditions for functions of Schrodinger operators,
    Ann. Henri Poincaré 20, no. 11 (2019), 3543-3562.
    DOI: https://doi.org/10.1007/s00023-019-00838-8
    preprint


62. P. Gerard, A. Pushnitski,
    Weighted model spaces and Schmidt subspaces of Hankel operators,
    J. Lond. Math. Soc. (2) 101, no. 1 (2020) 271-298.
    DOI: https://doi.org/10.1112/jlms.12270
    preprint


63. N. Miheisi, A. Pushnitski,
    Restriction theorems for Hankel operators,
    Studia Math. 254, no. 1 (2020), 1-21.
    DOI: https://doi.org/10.4064/sm181109-2-7
    preprint


64. P. Gerard, A. Pushnitski,
    The structure of Schmidt subspaces of Hankel operators: a short proof,
    Studia Math. 256, no. 1 (2021), 61-71.
    DOI: https://doi.org/10.4064/sm190717-7-2
    preprint


65. N. Nikolski, A. Pushnitski,
    Szegő-type limit theorems for "multiplicative Toeplitz" operators and non-Følner approximations,
    St.Petersburg Math. J. 32, no. 6 (2021), 1033–1050.
    preprint


66. O. F. Brevig, K. Perfekt, A. Pushnitski,
    The spectrum of some Hardy kernel matrices,
    to appear in Annales de l'Inst. Fourier,
    preprint


67. A. Pushnitski,
    The spectral density of Hardy kernel matrices,
    J. Operator Theory, 89, no. 1 (2023), 3-21.
    preprint


68. T. Hilberdink, A. Pushnitski,
    Spectral asymptotics for a family of LCM matrices,
    St.Petersburg Math. J. 34 (2023), 463-481.
    preprint


69. P. Gerard, A. Pushnitski,
    Unbounded Hankel operators and the flow of the cubic Szegő equation,
    Invent. Math. 232 (2023), 995–1026.
    preprint


70. P. Gerard, A. Pushnitski,
    An inverse problem for Hankel operators and turbulent solutions of the cubic Szegő equation on the line,
    to appear in J. of Eur. Math. Soc. (JEMS).
    preprint


71. P. Gerard, A. Pushnitski, S. Treil,
    An inverse spectral problem for non-compact Hankel operators with simple spectrum,
    to appear in Journal d'Analyse Mathematique.
    preprint


72. F. Štampach, A. Pushnitski,
    An inverse spectral problem for non-self-adjoint Jacobi matrices,
    Int. Math. Res. Notices, 2024, no. 7 (2024), 6106–6139.
    preprint


73. P. Gerard, A. Pushnitski,
    The cubic Szegő equation on the real line: explicit formula and well-posedness on the Hardy class,
    preprint


74. A. Pushnitski, A. Sobolev,
    Hankel operators with band spectra and elliptic functions,
    preprint


75. A. Pushnitski, I. Wigman,
    Eigenvalue clusters for the hemisphere Laplacian with variable Robin condition,
    preprint


76. T. Hilberdink, A. Pushnitski,
    Spectral asymptotics for a family of arithmetical matrices and connection to Beurling primes,
    to appear in Pure and Applied Functional Analysis (Fritz Gesztesy 70th birthday volume)
    preprint


77. A. Pushnitski,
    Three families of matrices,
    Exposit. Math. 42, no.2 (2024), 125546.
    preprint


78. F. Štampach, A. Pushnitski,
    A functional model and tridiagonalisation for symmetric anti-linear operators,
    preprint