Prof. Dr. Konstantin Pankrashkin

https://uol.de/pankrashkin


Veröffentlichungen | Publications

One may also check a list of my coauthors and my profiles: Google Scholar, MathSciNet, ORCID, ResearcherID, ResearchGate, Scopus, zbMATH

Papers

In press

  • D. Krejčiřík, V. Lotoreichik, K. Pankrashkin, M. Tušek: Spectral analysis of the multi-dimensional diffusion operator with random jumps from the boundary. J. Evol. Equ. (in press). Preprint arXiv.
  • 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.
  • M. Khalile, T. Ourmières-Bonafos, K. Pankrashkin: Effective operators for Robin eigenvalues in domains with corners. Ann. Institut Fourier (in press). Preprint arXiv.

2020

  • K. Pankrashkin: An eigenvalue estimate for a Robin p-Laplacian in C1 domains. Proc. Amer. Math. Soc. 148 (2020) 4471-4477. Preprint arXiv.
  • J. Behrndt, M. Holzmann, T. Ourmières-Bonafos, K. Pankrashkin: Two-dimensional Dirac operators with singular interactions supported on closed curves. J. Funct. Anal. 279 (2020) 108700. Preprint arXiv or hal.
  • B. Flamencourt, K. Pankrashkin: Strong coupling asymptotics for δ-interactions supported by curves with cusps. J. Math. Anal. Appl. 491 (2020) 124287. Preprint pdf or arXiv.
  • S. Egger, J. Kerner, K. Pankrashkin: Discrete spectrum of Schrödinger operators with potentials concentrated near conical surfaces. Lett. Math. Phys. 110 (2020) 945-968. Preprint arXiv (the preprint has a different title).
  • A. Moroianu, T. Ourmières-Bonafos, K. Pankrashkin: Dirac operators on hypersurfaces as large mass limits. Comm. Math. Phys. 374 (2020) 1963-2013. Preprint pdf or arXiv.

2019

  • 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. Journal (open access) or preprint hal.
  • H. Kovařík, K. Pankrashkin: Robin eigenvalues on domains with peaks. J. Differential Equations 267 (2019) 1600-1630. Preprint pdf or arXiv.
  • C. Cacciapuoti, K. Pankrashkin, A. Posilicano: Self-adjoint indefinite Laplacians. J. Anal. Math. 139 (2019) 155-177. Preprint arXiv.

2018

  • M. Holzmann, T. Ourmières-Bonafos, K. Pankrashkin: Dirac operators with Lorentz scalar shell interactions. Rev. Math. Phys. 30 (2018) 1850013. Preprint arXiv.
  • 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.
  • T. Ourmières-Bonafos, K. Pankrashkin: Discrete spectrum of interactions concentrated near conical surfaces. Appl. Anal. 97 (2018) 1628–1649. Preprint arXiv.
  • M. Khalile, K. Pankrashkin: Eigenvalues of Robin Laplacians in infinite sectors. Math. Nachr. 291 (2018) 928–965. Preprint arXiv.
  • V. Bruneau, K. Pankrashkin, N. Popoff: Eigenvalue counting function for Robin Laplacians on conical domains. J. Geom. Anal. 28 (2018) 123–151. Preprint arXiv.

2017

  • K. Pankrashkin: Eigenvalue inequalities and absence of threshold resonances for waveguide junctions. J. Math. Anal. Appl. 449 (2017) 907–925. Preprint arXiv.
  • H. Kovařík, K. Pankrashkin: On the p-Laplacian with Robin boundary conditions and boundary trace theorems. Calc. Var. PDE 56 (2017) 49. Preprint arXiv.
  • 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.

2016

  • 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 or arXiv.
  • 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.
  • 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 or arXiv.
  • 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 or pdf.

2015

  • K. Pankrashkin: An inequality for the maximum curvature through a geometric flow. Arch. Math. (Basel) 105 (2015) 297–300. Preprint pdf or arXiv.
  • 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 or arXiv or journal.
  • K. Pankrashkin, N. Popoff: Mean curvature bounds and eigenvalues of Robin Laplacians. Calc. Var. PDE 54 (2015) 1947–1961. Preprint pdf or arXiv or hal.
  • B. Helffer, K. Pankrashkin: Tunneling between corners for Robin Laplacians. J. London Math. Soc. 91 (2015) 225–248. Preprint pdf or arXiv or hal.

2014

  • 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 or journal.
  • K. Pankrashkin: A remark on the discriminant of Hill's equation and Herglotz functions. Arch. Math. (Basel) 102 (2014) 155–163. Preprint arXiv or pdf.
  • P. Exner, K. Pankrashkin: Strong coupling asymptotics for a singular Schrödinger operator with an interaction supported by an open arc. Comm. PDE 39 (2014) 193–212. Preprint arXiv or mp-arc.

2013

  • 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 or journal.
  • K. Pankrashkin: An example of unitary equivalence between self-adjoint extensions and their parameters. J. Funct. Anal. 265 (2013) 2910–2936. Preprint arXiv.
  • D. Borisov, K. Pankrashkin: Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones. J. Phys. A 46 (2013) 235203. Preprint arXiv.
  • 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 or journal.
  • D. Borisov, K. Pankrashkin: On the extrema of band functions in periodic waveguides. Funct. Anal. Appl. 47 (2013) 238–240.
  • 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.

2012

  • 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 or in Ulmer Seminare, Heft 17 (2012) 323-340.

2011

  • 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 or mp-arc .
  • K. Pankrashkin, S. Richard: Spectral and scattering theory for the Aharonov-Bohm operators. Rev. Math. Phys. 23 (2011) 53–81. Preprint arXiv.
  • K. Pankrashkin, S. Roganova, N. Yeganefar: Resolvent expansions on hybrid manifolds. Integral Equations Operator Theory 71 (2011) 199–223. Preprint arXiv .

2010

  • 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.

2009

  • K. Pankrashkin: Quasiperiodic surface Maryland models on quantum graphs. J. Phys. A 42 (2009) 265304. Preprint arXiv.
  • 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.
  • F. Klopp, K. Pankrashkin: Localization on quantum graphs with random edge lengths. Lett. Math. Phys. 87 (2009) 99–114. Preprint arXiv. Erratum: pdf

2008

  • K. Pankrashkin: Variational principle for Hamiltonians with degenerate bottom. I. Beltita, G. Nenciu, R. Purice (Eds.): Mathematical Results in Quantum Mechanics. Proceedings of the QMath10 Conference (World Scientific, 2008) 231–240. Preprint arXiv.
  • K. Pankrashkin: Localization in a quasiperiodic model on quantum graphs. 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.
  • F. Klopp, K. Pankrashkin: Localization on quantum graphs with random vertex couplings. J. Stat. Phys. 131 (2008) 651–673. Preprint arXiv or mp-arc.
  • 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.

2007

  • 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.
  • 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.
  • J. Brüning, V. Geyler, K. Pankrashkin: Explicit Green functions for spin-orbit Hamiltonians. J. Phys. A 40 (2007) F697–F704. Preprint arXiv.
  • 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.
  • J. Brüning, V. Geyler, K. Pankrashkin: Cantor and band spectra for periodic quantum graphs with magnetic fields. Comm. Math. Phys. 269 (2007) 87–105. Preprint arXiv.

2006

  • K. Pankrashkin: Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction. J. Math. Phys. 47 (2006) 112105. Preprint arXiv.
  • K. Pankrashkin: Resolvents of self-adjoint extensions with mixed boundary conditions. Rep. Math. Phys. 58 (2006) 207–221. Preprint arXiv.
  • K. Pankrashkin: Spectra of Schrödinger operators on equilateral quantum graphs. Lett. Math. Phys. 77 (2006) 139–154. Preprint arXiv.

2005

  • J. Brüning, V. Geyler, K. Pankrashkin: On-diagonal singularities of the Green functions for Schrödinger operators. J. Math. Phys. 46 (2005) 113508. Preprint arXiv.
  • K. Pankrashkin: Reducible boundary conditions in coupled channels. J. Phys. A 38 (2005) 8979–8992. Preprint arXiv.
  • 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
  • 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.

2004

  • K. Pankrashkin: On semiclassical dispersion relations of Harper-like operators. J. Phys. A 37 (2004) 11681–11698. Preprint arXiv.
  • S. Dobrokhotov, K. Pankrashkin, E. Semenov: On Maslov's conjecture about square root type singular solutions of the shallow water equations. A. Delcroix, M. Hasler, J.-A. Marti, V. Valmorin (Eds.): Nonlinear Algebraic Analysis and Applications (Cambridge Sci. Publ., 2004) 73–88. Preprint arXiv.

2003

  • 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 this preprint.

2002

  • 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.
  • 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.

2001

  • K. Pankrashkin: Locality of quadratic forms for point perturbations of Schrödinger operators. Math. Notes 70:3 (2001) 384–391.
  • 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.
  • K. Pankrashkin, M. Poteryakhin: Short-wavelength asymptotics for the low Landau zones of the two-dimensional magnetic Schrödinger operator. I. V. Andronov (Ed.) : Proceedings of the international seminar "Day on Diffraction – 2001" (Saint-Petersburg Univ., 2001) 202–210. Book: link.
  • 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.

1999

  • V. Geyler, K. Pankrashkin: On fractal structure of the spectrum for periodic point perturbations of the Schrödinger operator with a uniform magnetic field. 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. Preprint pdf.

Other publications

  • U. Boscain, A. Kostenko, K. Pankrashkin (Eds.): Mini-workshop “Self-adjoint extensions in new settings”. Oberwolfach Reports 16 (2019) no. 4, 2911-2950.
  • V. Bonnaillie-Noël, H. Kovařík, K. Pankrashkin (Eds.): Mini-workshop “Eigenvalue problems in surface superconductivity”. Oberwolfach Reports 11 (2014) no. 4, 3015-3057.
  • J. Behrndt, K. Pankrashkin, O. Post (Eds.): Mini-workshop “Boundary value problems and spectral geometry”. Oberwolfach Reports 9 (2012) no. 1, 43–76.
(Stand: 27.11.2020)