Konstantin Pankrashkin

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Publications

Papers

Please note:

  1. J. Behrndt, M. Holzmann, T. Ourmières-Bonafos, K. Pankrashkin: Two-dimensional Dirac operators with singular interactions supported on closed curves
    Preprint arXiv:1907.05436 or hal-02181432
  2. K. Pankrashkin: On self-adjoint realizations of sign-indefinite Laplacians
    J. Faupin, M. Mantoiu, V. Nistor (Eds.): Proceedings "Spectral theory and mathematical physics", Rev. Roumaine Math. Pures Appl. 64:2-3 (2019) 345-372
    Preprint hal-01960406
  3. S. Egger, J. Kerner, K. Pankrashkin: Bound states of a pair of particles on the half-line with a general interaction potential
    J. Spectral Theory (in press)
    Preprint arXiv:1812.06500
  4. A. Moroianu, T. Ourmières-Bonafos, K. Pankrashkin: Dirac operators on hypersurfaces as large mass limits
    Preprint arXiv:1811.03340
  5. M. Khalile, T. Ourmières-Bonafos, K. Pankrashkin: Effective operators for Robin eigenvalues in domains with corners
    Preprint arXiv:1809.04998
  6. H. Kovařík, K. Pankrashkin: Robin eigenvalues on domains with peaks
    J. Differential Equations 267 (2019) 1600-1630
    Preprint arXiv:1803.09295
  7. M. Holzmann, T. Ourmières-Bonafos, K. Pankrashkin: Dirac operators with Lorentz scalar shell interactions
    Rev. Math. Phys. 30 (2018) 1850013.
    Preprint arXiv:1711.00746
  8. T. Ourmières-Bonafos, K. Pankrashkin, F. Pizzichillo: Spectral asymptotics for δ-interactions on sharp cones
    J. Math. Anal. Appl. 458 (2018) 566–589.
    Preprint arXiv:1707.01465
  9. T. Ourmières-Bonafos, K. Pankrashkin: Discrete spectrum of interactions concentrated near conical surfaces
    Appl. Anal. 97 (2018) 1628–1649.
    Preprint arXiv:1612.01798
  10. C. Cacciapuoti, K. Pankrashkin, A. Posilicano: Self-adjoint indefinite Laplacians
    J. Anal. Math. (in press).
    Preprint arXiv:1611.00696
  11. M. Khalile, K. Pankrashkin: Eigenvalues of Robin Laplacians in infinite sectors
    Math. Nachr. 291 (2018) 928–965.
    Preprint arXiv:1607.06848
  12. K. Pankrashkin: Eigenvalue inequalities and absence of threshold resonances for waveguide junctions
    J. Math. Anal. Appl. 449 (2017) 907–925
    Preprint arXiv:1606.09620
  13. H. Kovařík, K. Pankrashkin: On the p-Laplacian with Robin boundary conditions and boundary trace theorems
    Calc. Var. PDE 56 (2017) 49
    Preprint arXiv:1603.01737
  14. V. Bruneau, K. Pankrashkin, N. Popoff: Eigenvalue counting function for Robin Laplacians on conical domains
    J. Geom. Anal. 28 (2018) 123–151
    Preprint arXiv:1602.07448
  15. K. Pankrashkin: Variational proof of the existence of eigenvalues for star graphs
    J. Dittrich, H. Kovařík, A. Laptev (Eds.): Functional Analysis and Operator Theory for Quantum Physics. Pavel Exner Anniversary Volume (EMS Series of Congress Reports, vol. 12, 2017) 447–458
    Preprint arXiv:1511.09227
  16. K. Pankrashkin: On the discrete spectrum of Robin Laplacians in conical domains
    Special issue "Spectral problems" (edited by R. Ibragimov, V. Vougalter, M.W. Wong)
    Math. Model. Nat. Phenom. 11 no. 2 (2016) 100–110
    Preprint pdf (300 kB) or arXiv:1507.08980
  17. J. Dittrich, P. Exner, C. Kühn, K. Pankrashkin: On eigenvalue asymptotics for strong δ-interactions supported by surfaces with boundaries
    Asymptot. Anal. 97 (2016) 1–25
    Preprint arXiv:1506.06583
  18. K. Pankrashkin, N. Popoff: An effective Hamiltonian for the eigenvalue asymptotics of the Robin Laplacian with a large parameter
    J. Math. Pures Appl. 106 (2016) 615–650
    Preprint pdf (300 kB) or arXiv:1502.00877
  19. K. Pankrashkin: An inequality for the maximum curvature through a geometric flow
    Arch. Math. (Basel) 105 (2015) 297–300
    Preprint pdf (100 kB) or arXiv:1501.03792
  20. K. Pankrashkin: On the Robin eigenvalues of the Laplacian in the exterior of a convex polygon
    Nanosystems: Phys. Chem. Math. 6 (2015) 46–56
    Preprint pdf (200 kB) or arXiv:1411.1956 or journal
  21. K. Pankrashkin, N. Popoff: Mean curvature bounds and eigenvalues of Robin Laplacians
    Calc. Var. PDE 54 (2015) 1947–1961
    Preprint pdf (250 kB) or arXiv:1407.3087 or hal-01022945
  22. B. Helffer, K. Pankrashkin: Tunneling between corners for Robin Laplacians
    J. London Math. Soc. 91 (2015) 225–248
    Preprint pdf (330 kB) or arXiv:1404.4765 or hal-00980575
  23. K. Pankrashkin, S. Richard: One-dimensional Dirac operators with zero-range interactions: spectral, scattering, and topological results
    J. Math. Phys. 55 (2014) 062305
    Preprint arXiv:1402.1542 or journal
  24. K. Pankrashkin: A remark on the discriminant of Hill's equation and Herglotz functions
    Arch. Math. (Basel) 102 (2014) 155–163
    Preprint arXiv:1401.1662 or pdf (130 kB)
  25. D. Lenz, K. Pankrashkin: New relations between discrete and continuous transition operators on (metric) graphs
    Integral Equations Operator Theory 84 (2016) 151–181
    Preprint arXiv:1305.7491 or pdf (250 kB)
  26. K. Pankrashkin: On the asymptotics of the principal eigenvalue for a Robin problem with a large parameter in planar domains
    Nanosystems: Phys. Chem. Math. 4 (2013) 474–483
    Preprint arXiv:1305.3293 or journal
  27. K. Pankrashkin: An example of unitary equivalence between self-adjoint extensions and their parameters
    J. Funct. Anal. 265 (2013) 2910–2936
    Preprint arXiv:1212.6798
  28. D. Borisov, K. Pankrashkin: Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones
    J. Phys. A 46 (2013) 235203 (featured article)
    Preprint arXiv:1211.5786
  29. P. Exner, K. Pankrashkin: Strong coupling asymptotics for a singular Schrödinger operator with an interaction supported by an open arc
    Commun. PDE 39 (2014) 193–212
    Preprint arXiv:1207.2271 or mp-arc/12-74
  30. A. Goriunov, V. Mikhailets, K. Pankrashkin: Formally self-adjoint quasi-differential operators and boundary value problems
    Electronic J. Differential Equations 2013 (2013) no. 101, 1–16
    Preprint arXiv:1205.1810 or journal
  31. D. Borisov, K. Pankrashkin: On the extrema of band functions in periodic waveguides
    Funct. Anal. Appl. 47 (2013) 238–240
  32. D. Borisov, K. Pankrashkin: Gap opening and split band edges in waveguides coupled by a periodic system of small windows
    Math. Notes 93 (2013) 660–675
    Preprint arXiv:1203.0201
  33. K. Pankrashkin: Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures
    J. Math. Anal. Appl. 396 (2012) 640–655
    Preprint arXiv:1109.0712 or in Ulmer Seminare, Heft 17 (2012) 323-340.
  34. J. Kellendonk, K. Pankrashkin, S. Richard: Levinson's theorem and higher degree traces for Aharonov-Bohm operators
    J. Math. Phys. 52 (2011) 052102
    Preprint arXiv:1012.3215 or mp-arc/10-198
  35. K. Pankrashkin, S. Richard: Spectral and scattering theory for the Aharonov-Bohm operators
    Rev. Math. Phys. 23 (2011) 53–81
    Preprint arxiv:0911.4715
  36. K. Pankrashkin, S. Roganova, N. Yeganefar: Resolvent expansions on hybrid manifolds
    Integral Equations Operator Theory 71 (2011) 199–223
    Preprint arxiv:0911.3282
  37. K. Pankrashkin: On the spectrum of a waveguide with periodic cracks
    Special issue "Spectral and transport properties of quantum systems" in memory of Pierre Duclos (edited by J.-M. Combes, P. Exner, V. A. Zagrebnov)
    J. Phys. A 43 (2010) 474030
    Preprint arxiv:1007.3656
  38. K. Pankrashkin: Quasiperiodic surface Maryland models on quantum graphs
    J. Phys. A 42 (2009) 265304
    Preprint arXiv:0811.3308
  39. B. Helffer, K. Pankrashkin: Semiclassical reduction for magnetic Schrödinger operator with periodic zero-range potentials and applications
    Asymptot. Anal. 63 (2009) 1–27
    Preprint arXiv:0802.1414
  40. F. Klopp, K. Pankrashkin: Localization on quantum graphs with random edge lengths
    Lett. Math. Phys. 87 (2009) 99–114
    Preprint arXiv:0810.1006. Erratum: pdf
  41. K. Pankrashkin: Variational principle for Hamiltonians with degenerate bottom
    In the book I. Beltita, G. Nenciu, R. Purice (Eds.): Mathematical Results in Quantum Mechanics. Proceedings of the QMath10 Conference (World Scientific, 2008) 231–240
    Preprint arXiv:0710.4790
  42. K. Pankrashkin: Localization in a quasiperiodic model on quantum graphs
    In the book P. Exner, J. P. Keating, P. Kuchment, T. Sunada, A. Teplyaev (Eds): Analysis on Graphs and its Applications (Proc. Symp. Pure Math., vol. 77, AMS, 2008) 459–467
    Preprint arXiv:0707.2041
  43. F. Klopp, K. Pankrashkin: Localization on quantum graphs with random vertex couplings
    J. Stat. Phys. 131 (2008) 651–673
    Preprint arXiv:0710.3065 or mp-arc/07-243
  44. J. Brüning, V. Geyler, K. Pankrashkin: Spectra of self-adjoint extensions and applications to solvable Schrödinger operators
    Rev. Math. Phys. 20 (2008) 1–70
    Preprint arXiv:math-ph/0611088
  45. J. Brüning, V. Geyler, K. Pankrashkin: On the discrete spectrum of spin-orbit Hamiltonians with singular interactions
    Russian J. Math. Phys. 14 (2007) 423–429
    Preprint arXiv:0709.0213
  46. J. Brüning, V. Geyler, K. Pankrashkin: Continuity properties of integral kernels associated with Schrödinger operators on manifolds
    Annales Henri Poincaré 8 (2007) 781–816
    Preprint arXiv:math-ph/0410042
  47. J. Brüning, V. Geyler, K. Pankrashkin: Explicit Green functions for spin-orbit Hamiltonians
    J. Phys. A 40 (2007) F697–F704
    Preprint arXiv:0704.2877
  48. J. Brüning, V. Geyler, K. Pankrashkin: On the number of bound states for weak perturbations of spin-orbit Hamitonians
    J. Phys. A 40 (2007) F113–F117
    Preprint arXiv:math-ph/0611080
  49. J. Brüning, V. Geyler, K. Pankrashkin: Cantor and band spectra for periodic quantum graphs with magnetic fields
    Commun. Math. Phys. 269 (2007) 87–105
    Preprint arXiv:math-ph/0511057
  50. K. Pankrashkin: Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction
    J. Math. Phys. 47 (2006) 112105
    Preprint arXiv:math-ph/0607034
  51. K. Pankrashkin: Resolvents of self-adjoint extensions with mixed boundary conditions
    Rep. Math. Phys. 58 (2006) 207–221
    Preprint arXiv:math.FA/0412431
  52. K. Pankrashkin: Spectra of Schrödinger operators on equilateral quantum graphs
    Lett. Math. Phys. 77 (2006) 139–154
    Preprint arXiv:math-ph/0512090
  53. J. Brüning, V. Geyler, K. Pankrashkin: On-diagonal singularities of the Green functions for Schrödinger operators
    J. Math. Phys. 46 (2005) 113508
    Preprint arXiv:math-ph/0411078
  54. K. Pankrashkin: Reducible boundary conditions in coupled channels
    J. Phys. A 38 (2005) 8979–8992
    Preprint arXiv:math-ph/0506009
  55. J. Brüning, V. Geyler, K. Pankrashkin: Continuity and asymptotic behavior of integral kernels related to Schrödinger operators on manifolds
    Math. Notes 78:2 (2005) 285–288
  56. S. Albeverio, K. Pankrashkin: A remark on Krein's resolvent formula and boundary conditions
    Special issue "Singular interactions in quantum mechanics: solvable models" (edited by G. Dell'Antonio, P. Exner, V. Geyler)
    J. Phys. A 38 (2005) 4859–4864
    Preprint arXiv:math-ph/0408021
  57. K. Pankrashkin: On semiclassical dispersion relations of Harper-like operators
    J. Phys. A 37 (2004) 11681–11698
    Preprint arXiv:math-ph/0401049
  58. S. Dobrokhotov, K. Pankrashkin, E. Semenov: On Maslov's conjecture about square root type singular solutions of the shallow water equations
    In the book A. Delcroix, M. Hasler, J.-A. Marti, V. Valmorin (Eds.): Nonlinear Algebraic Analysis and Applications (Cambridge Sci. Publ., 2004) 73–88
    Preprint arXiv:math-ph/0404003
  59. J. Brüning, S. Dobrokhotov, V. Geyler, K. Pankrashkin: Hall conductivity of the minbands lying at the wings of Landau levels
    JETP Letters 77:11 (2003) 616–618
    See also arXiv:cond-mat/0205443
  60. J. Brüning, S. Dobrokhotov, K. Pankrashkin: The asymptotic form of the lower Landau bands in a strong magnetic field
    Theor. Math. Phys. 131:2 (2002) 705–728
  61. J. Brüning, S. Dobrokhotov, K. Pankrashkin: The spectral asymptotics of the two-dimensional Schrödinger operator with a strong magnetic field
    Russian J. Math. Phys. 9 (2002), Part I: 14–49, Part II: 400–416
    Preprint arXiv:math-ph/0411012
  62. K. Pankrashkin: Locality of quadratic forms for point perturbations of Schrödinger operators
    Math. Notes 70:3 (2001) 384–391
  63. S. Dobrokhotov, K. Pankrashkin, E. Semenov: On Maslov's conjecture on the structure of weak point singularities for the shallow water equations
    Doklady Math. 64:1 (2001) 127–130.
  64. K. Pankrashkin, M. Poteryakhin: Short-wavelength asymptotics for the low Landau zones of the two-dimensional magnetic Schrödinger operator.
    In I. V. Andronov (Ed.) : Proceedings of the international seminar "Day on Diffraction – 2001" (Saint-Petersburg Univ., 2001) 202–210.
    Book: link
  65. S. Dobrokhotov, K. Pankrashkin, E. Semenov: Proof of Maslov's conjecture about the structure of weak point singular solutions of the shallow water equations
    Russian J. Math. Phys. 8 (2001) 25–54.
  66. V. Geyler, K. Pankrashkin: On fractal structure of the spectrum for periodic point perturbations of the Schrödinger operator with a uniform magnetic field
    In the book J. Dittrich, P. Exner, M. Tater (Eds.): Mathematical Results in Quantum Mechanics. QMath7 conference (Operator Theory: Adv. Appl., vol. 108, Birkhäuser, Basel, 1999) 259–265
    [PDF, 50 kB]

Theses


Other publications


Konstantin Pankrashkin http://www.math.u-psud.fr/~pankrashkin/